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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Proof: DP Processor: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U101(tt(),V1,V2)) -> isNatKind#(V1) active#(U101(tt(),V1,V2)) -> U102#(isNatKind(V1),V1,V2) active#(U101(tt(),V1,V2)) -> mark#(U102(isNatKind(V1),V1,V2)) active#(U102(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U102(tt(),V1,V2)) -> U103#(isNatIListKind(V2),V1,V2) active#(U102(tt(),V1,V2)) -> mark#(U103(isNatIListKind(V2),V1,V2)) active#(U103(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U103(tt(),V1,V2)) -> U104#(isNatIListKind(V2),V1,V2) active#(U103(tt(),V1,V2)) -> mark#(U104(isNatIListKind(V2),V1,V2)) active#(U104(tt(),V1,V2)) -> isNat#(V1) active#(U104(tt(),V1,V2)) -> U105#(isNat(V1),V2) active#(U104(tt(),V1,V2)) -> mark#(U105(isNat(V1),V2)) active#(U105(tt(),V2)) -> isNatIList#(V2) active#(U105(tt(),V2)) -> U106#(isNatIList(V2)) active#(U105(tt(),V2)) -> mark#(U106(isNatIList(V2))) active#(U106(tt())) -> mark#(tt()) active#(U11(tt(),V1)) -> isNatIListKind#(V1) active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U111(tt(),L,N)) -> isNatIListKind#(L) active#(U111(tt(),L,N)) -> U112#(isNatIListKind(L),L,N) active#(U111(tt(),L,N)) -> mark#(U112(isNatIListKind(L),L,N)) active#(U112(tt(),L,N)) -> isNat#(N) active#(U112(tt(),L,N)) -> U113#(isNat(N),L,N) active#(U112(tt(),L,N)) -> mark#(U113(isNat(N),L,N)) active#(U113(tt(),L,N)) -> isNatKind#(N) active#(U113(tt(),L,N)) -> U114#(isNatKind(N),L) active#(U113(tt(),L,N)) -> mark#(U114(isNatKind(N),L)) active#(U114(tt(),L)) -> length#(L) active#(U114(tt(),L)) -> s#(length(L)) active#(U114(tt(),L)) -> mark#(s(length(L))) active#(U12(tt(),V1)) -> isNatList#(V1) active#(U12(tt(),V1)) -> U13#(isNatList(V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U121(tt(),IL)) -> isNatIListKind#(IL) active#(U121(tt(),IL)) -> U122#(isNatIListKind(IL)) active#(U121(tt(),IL)) -> mark#(U122(isNatIListKind(IL))) active#(U122(tt())) -> mark#(nil()) active#(U13(tt())) -> mark#(tt()) active#(U131(tt(),IL,M,N)) -> isNatIListKind#(IL) active#(U131(tt(),IL,M,N)) -> U132#(isNatIListKind(IL),IL,M,N) active#(U131(tt(),IL,M,N)) -> mark#(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#(U132(tt(),IL,M,N)) -> mark#(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#(U133(tt(),IL,M,N)) -> mark#(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#(U134(tt(),IL,M,N)) -> mark#(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#(U135(tt(),IL,M,N)) -> mark#(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#(U136(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) active#(U21(tt(),V1)) -> isNatKind#(V1) active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> isNat#(V1) active#(U22(tt(),V1)) -> U23#(isNat(V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) active#(U31(tt(),V)) -> isNatIListKind#(V) active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) active#(U32(tt(),V)) -> isNatList#(V) active#(U32(tt(),V)) -> U33#(isNatList(V)) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) active#(U33(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> isNatKind#(V1) active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) active#(U44(tt(),V1,V2)) -> isNat#(V1) active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) active#(U45(tt(),V2)) -> isNatIList#(V2) active#(U45(tt(),V2)) -> U46#(isNatIList(V2)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> isNatIListKind#(V2) active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) active#(U61(tt(),V2)) -> isNatIListKind#(V2) active#(U61(tt(),V2)) -> U62#(isNatIListKind(V2)) 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)) -> isNatKind#(V1) active#(U91(tt(),V1,V2)) -> U92#(isNatKind(V1),V1,V2) active#(U91(tt(),V1,V2)) -> mark#(U92(isNatKind(V1),V1,V2)) active#(U92(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U92(tt(),V1,V2)) -> U93#(isNatIListKind(V2),V1,V2) active#(U92(tt(),V1,V2)) -> mark#(U93(isNatIListKind(V2),V1,V2)) active#(U93(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U93(tt(),V1,V2)) -> U94#(isNatIListKind(V2),V1,V2) active#(U93(tt(),V1,V2)) -> mark#(U94(isNatIListKind(V2),V1,V2)) active#(U94(tt(),V1,V2)) -> isNat#(V1) active#(U94(tt(),V1,V2)) -> U95#(isNat(V1),V2) active#(U94(tt(),V1,V2)) -> mark#(U95(isNat(V1),V2)) active#(U95(tt(),V2)) -> isNatList#(V2) active#(U95(tt(),V2)) -> U96#(isNatList(V2)) active#(U95(tt(),V2)) -> mark#(U96(isNatList(V2))) active#(U96(tt())) -> mark#(tt()) active#(isNat(0())) -> mark#(tt()) active#(isNat(length(V1))) -> isNatIListKind#(V1) active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) active#(isNat(s(V1))) -> isNatKind#(V1) active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) active#(isNatIList(V)) -> isNatIListKind#(V) active#(isNatIList(V)) -> U31#(isNatIListKind(V),V) active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V)) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1) active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) active#(isNatIListKind(nil())) -> mark#(tt()) active#(isNatIListKind(zeros())) -> mark#(tt()) active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1) active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) active#(isNatIListKind(take(V1,V2))) -> isNatKind#(V1) active#(isNatIListKind(take(V1,V2))) -> U61#(isNatKind(V1),V2) active#(isNatIListKind(take(V1,V2))) -> mark#(U61(isNatKind(V1),V2)) active#(isNatKind(0())) -> mark#(tt()) active#(isNatKind(length(V1))) -> isNatIListKind#(V1) active#(isNatKind(length(V1))) -> U71#(isNatIListKind(V1)) active#(isNatKind(length(V1))) -> mark#(U71(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> isNatKind#(V1) active#(isNatKind(s(V1))) -> U81#(isNatKind(V1)) active#(isNatKind(s(V1))) -> mark#(U81(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> isNatKind#(V1) active#(isNatList(cons(V1,V2))) -> U91#(isNatKind(V1),V1,V2) active#(isNatList(cons(V1,V2))) -> mark#(U91(isNatKind(V1),V1,V2)) active#(isNatList(take(V1,V2))) -> isNatKind#(V1) active#(isNatList(take(V1,V2))) -> U101#(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))) -> isNatList#(L) active#(length(cons(N,L))) -> U111#(isNatList(L),L,N) active#(length(cons(N,L))) -> mark#(U111(isNatList(L),L,N)) active#(take(0(),IL)) -> isNatIList#(IL) active#(take(0(),IL)) -> U121#(isNatIList(IL),IL) active#(take(0(),IL)) -> mark#(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#(take(s(M),cons(N,IL))) -> mark#(U131(isNatIList(IL),IL,M,N)) mark#(zeros()) -> active#(zeros()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(0()) -> active#(0()) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U101(X1,X2,X3)) -> U101#(mark(X1),X2,X3) mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3)) mark#(tt()) -> active#(tt()) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> U102#(mark(X1),X2,X3) mark#(U102(X1,X2,X3)) -> active#(U102(mark(X1),X2,X3)) mark#(isNatKind(X)) -> active#(isNatKind(X)) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> U103#(mark(X1),X2,X3) mark#(U103(X1,X2,X3)) -> active#(U103(mark(X1),X2,X3)) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> U104#(mark(X1),X2,X3) mark#(U104(X1,X2,X3)) -> active#(U104(mark(X1),X2,X3)) mark#(U105(X1,X2)) -> mark#(X1) mark#(U105(X1,X2)) -> U105#(mark(X1),X2) mark#(U105(X1,X2)) -> active#(U105(mark(X1),X2)) mark#(isNat(X)) -> active#(isNat(X)) mark#(U106(X)) -> mark#(X) mark#(U106(X)) -> U106#(mark(X)) mark#(U106(X)) -> active#(U106(mark(X))) mark#(isNatIList(X)) -> active#(isNatIList(X)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> U12#(mark(X1),X2) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) mark#(U111(X1,X2,X3)) -> mark#(X1) mark#(U111(X1,X2,X3)) -> U111#(mark(X1),X2,X3) mark#(U111(X1,X2,X3)) -> active#(U111(mark(X1),X2,X3)) mark#(U112(X1,X2,X3)) -> mark#(X1) mark#(U112(X1,X2,X3)) -> U112#(mark(X1),X2,X3) mark#(U112(X1,X2,X3)) -> active#(U112(mark(X1),X2,X3)) mark#(U113(X1,X2,X3)) -> mark#(X1) mark#(U113(X1,X2,X3)) -> U113#(mark(X1),X2,X3) mark#(U113(X1,X2,X3)) -> active#(U113(mark(X1),X2,X3)) mark#(U114(X1,X2)) -> mark#(X1) mark#(U114(X1,X2)) -> U114#(mark(X1),X2) mark#(U114(X1,X2)) -> active#(U114(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(length(X)) -> mark#(X) mark#(length(X)) -> length#(mark(X)) mark#(length(X)) -> active#(length(mark(X))) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> U13#(mark(X)) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U121(X1,X2)) -> mark#(X1) mark#(U121(X1,X2)) -> U121#(mark(X1),X2) mark#(U121(X1,X2)) -> active#(U121(mark(X1),X2)) mark#(U122(X)) -> mark#(X) mark#(U122(X)) -> U122#(mark(X)) mark#(U122(X)) -> active#(U122(mark(X))) mark#(nil()) -> active#(nil()) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> U131#(mark(X1),X2,X3,X4) mark#(U131(X1,X2,X3,X4)) -> active#(U131(mark(X1),X2,X3,X4)) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> U132#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> active#(U132(mark(X1),X2,X3,X4)) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> U133#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> active#(U133(mark(X1),X2,X3,X4)) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> U134#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> active#(U134(mark(X1),X2,X3,X4)) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> U135#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> active#(U135(mark(X1),X2,X3,X4)) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> U136#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> active#(U136(mark(X1),X2,X3,X4)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> U21#(mark(X1),X2) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> U22#(mark(X1),X2) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> U23#(mark(X)) mark#(U23(X)) -> active#(U23(mark(X))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> U32#(mark(X1),X2) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> U33#(mark(X)) mark#(U33(X)) -> active#(U33(mark(X))) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> U45#(mark(X1),X2) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> U46#(mark(X)) mark#(U46(X)) -> active#(U46(mark(X))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> U52#(mark(X)) mark#(U52(X)) -> active#(U52(mark(X))) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> U71#(mark(X)) mark#(U71(X)) -> active#(U71(mark(X))) mark#(U81(X)) -> mark#(X) mark#(U81(X)) -> U81#(mark(X)) mark#(U81(X)) -> active#(U81(mark(X))) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> U91#(mark(X1),X2,X3) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> U92#(mark(X1),X2,X3) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> U93#(mark(X1),X2,X3) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> U94#(mark(X1),X2,X3) mark#(U94(X1,X2,X3)) -> active#(U94(mark(X1),X2,X3)) mark#(U95(X1,X2)) -> mark#(X1) mark#(U95(X1,X2)) -> U95#(mark(X1),X2) mark#(U95(X1,X2)) -> active#(U95(mark(X1),X2)) mark#(U96(X)) -> mark#(X) mark#(U96(X)) -> U96#(mark(X)) mark#(U96(X)) -> active#(U96(mark(X))) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3) U101#(active(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,active(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3) U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,mark(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,mark(X3)) -> U102#(X1,X2,X3) U102#(active(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,active(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,active(X3)) -> U102#(X1,X2,X3) isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,mark(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,mark(X3)) -> U103#(X1,X2,X3) U103#(active(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,active(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,active(X3)) -> U103#(X1,X2,X3) isNatIListKind#(mark(X)) -> isNatIListKind#(X) isNatIListKind#(active(X)) -> isNatIListKind#(X) U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,mark(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,mark(X3)) -> U104#(X1,X2,X3) U104#(active(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,active(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,active(X3)) -> U104#(X1,X2,X3) U105#(mark(X1),X2) -> U105#(X1,X2) U105#(X1,mark(X2)) -> U105#(X1,X2) U105#(active(X1),X2) -> U105#(X1,X2) U105#(X1,active(X2)) -> U105#(X1,X2) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) U106#(mark(X)) -> U106#(X) U106#(active(X)) -> U106#(X) isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) U111#(mark(X1),X2,X3) -> U111#(X1,X2,X3) U111#(X1,mark(X2),X3) -> U111#(X1,X2,X3) U111#(X1,X2,mark(X3)) -> U111#(X1,X2,X3) U111#(active(X1),X2,X3) -> U111#(X1,X2,X3) U111#(X1,active(X2),X3) -> U111#(X1,X2,X3) U111#(X1,X2,active(X3)) -> U111#(X1,X2,X3) U112#(mark(X1),X2,X3) -> U112#(X1,X2,X3) U112#(X1,mark(X2),X3) -> U112#(X1,X2,X3) U112#(X1,X2,mark(X3)) -> U112#(X1,X2,X3) U112#(active(X1),X2,X3) -> U112#(X1,X2,X3) U112#(X1,active(X2),X3) -> U112#(X1,X2,X3) U112#(X1,X2,active(X3)) -> U112#(X1,X2,X3) U113#(mark(X1),X2,X3) -> U113#(X1,X2,X3) U113#(X1,mark(X2),X3) -> U113#(X1,X2,X3) U113#(X1,X2,mark(X3)) -> U113#(X1,X2,X3) U113#(active(X1),X2,X3) -> U113#(X1,X2,X3) U113#(X1,active(X2),X3) -> U113#(X1,X2,X3) U113#(X1,X2,active(X3)) -> U113#(X1,X2,X3) U114#(mark(X1),X2) -> U114#(X1,X2) U114#(X1,mark(X2)) -> U114#(X1,X2) U114#(active(X1),X2) -> U114#(X1,X2) U114#(X1,active(X2)) -> U114#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) U13#(mark(X)) -> U13#(X) U13#(active(X)) -> U13#(X) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) U121#(mark(X1),X2) -> U121#(X1,X2) U121#(X1,mark(X2)) -> U121#(X1,X2) U121#(active(X1),X2) -> U121#(X1,X2) U121#(X1,active(X2)) -> U121#(X1,X2) U122#(mark(X)) -> U122#(X) U122#(active(X)) -> U122#(X) U131#(mark(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,mark(X2),X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,mark(X3),X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,X3,mark(X4)) -> U131#(X1,X2,X3,X4) U131#(active(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,active(X2),X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,active(X3),X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,X3,active(X4)) -> U131#(X1,X2,X3,X4) U132#(mark(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,mark(X2),X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,mark(X3),X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,X3,mark(X4)) -> U132#(X1,X2,X3,X4) U132#(active(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,active(X2),X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,active(X3),X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,X3,active(X4)) -> U132#(X1,X2,X3,X4) U133#(mark(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,mark(X2),X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,mark(X3),X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,X3,mark(X4)) -> U133#(X1,X2,X3,X4) U133#(active(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,active(X2),X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,active(X3),X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,X3,active(X4)) -> U133#(X1,X2,X3,X4) U134#(mark(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,mark(X2),X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,mark(X3),X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,X3,mark(X4)) -> U134#(X1,X2,X3,X4) U134#(active(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,active(X2),X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,active(X3),X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,X3,active(X4)) -> U134#(X1,X2,X3,X4) U135#(mark(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,mark(X2),X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,mark(X3),X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,X3,mark(X4)) -> U135#(X1,X2,X3,X4) U135#(active(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,active(X2),X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,active(X3),X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,X3,active(X4)) -> U135#(X1,X2,X3,X4) U136#(mark(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,mark(X2),X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,mark(X3),X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,X3,mark(X4)) -> U136#(X1,X2,X3,X4) U136#(active(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,active(X2),X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,active(X3),X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,X3,active(X4)) -> U136#(X1,X2,X3,X4) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) U21#(mark(X1),X2) -> U21#(X1,X2) U21#(X1,mark(X2)) -> U21#(X1,X2) U21#(active(X1),X2) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) U32#(active(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) U33#(mark(X)) -> U33#(X) U33#(active(X)) -> U33#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) U45#(active(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) U46#(mark(X)) -> U46#(X) U46#(active(X)) -> U46#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X)) -> U71#(X) U71#(active(X)) -> U71#(X) U81#(mark(X)) -> U81#(X) U81#(active(X)) -> U81#(X) U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,mark(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3) U91#(active(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,active(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3) U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,mark(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3) U92#(active(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,active(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3) U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,mark(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3) U93#(active(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,active(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3) U94#(mark(X1),X2,X3) -> U94#(X1,X2,X3) U94#(X1,mark(X2),X3) -> U94#(X1,X2,X3) U94#(X1,X2,mark(X3)) -> U94#(X1,X2,X3) U94#(active(X1),X2,X3) -> U94#(X1,X2,X3) U94#(X1,active(X2),X3) -> U94#(X1,X2,X3) U94#(X1,X2,active(X3)) -> U94#(X1,X2,X3) U95#(mark(X1),X2) -> U95#(X1,X2) U95#(X1,mark(X2)) -> U95#(X1,X2) U95#(active(X1),X2) -> U95#(X1,X2) U95#(X1,active(X2)) -> U95#(X1,X2) U96#(mark(X)) -> U96#(X) U96#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) TDG Processor: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U101(tt(),V1,V2)) -> isNatKind#(V1) active#(U101(tt(),V1,V2)) -> U102#(isNatKind(V1),V1,V2) active#(U101(tt(),V1,V2)) -> mark#(U102(isNatKind(V1),V1,V2)) active#(U102(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U102(tt(),V1,V2)) -> U103#(isNatIListKind(V2),V1,V2) active#(U102(tt(),V1,V2)) -> mark#(U103(isNatIListKind(V2),V1,V2)) active#(U103(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U103(tt(),V1,V2)) -> U104#(isNatIListKind(V2),V1,V2) active#(U103(tt(),V1,V2)) -> mark#(U104(isNatIListKind(V2),V1,V2)) active#(U104(tt(),V1,V2)) -> isNat#(V1) active#(U104(tt(),V1,V2)) -> U105#(isNat(V1),V2) active#(U104(tt(),V1,V2)) -> mark#(U105(isNat(V1),V2)) active#(U105(tt(),V2)) -> isNatIList#(V2) active#(U105(tt(),V2)) -> U106#(isNatIList(V2)) active#(U105(tt(),V2)) -> mark#(U106(isNatIList(V2))) active#(U106(tt())) -> mark#(tt()) active#(U11(tt(),V1)) -> isNatIListKind#(V1) active#(U11(tt(),V1)) -> U12#(isNatIListKind(V1),V1) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) active#(U111(tt(),L,N)) -> isNatIListKind#(L) active#(U111(tt(),L,N)) -> U112#(isNatIListKind(L),L,N) active#(U111(tt(),L,N)) -> mark#(U112(isNatIListKind(L),L,N)) active#(U112(tt(),L,N)) -> isNat#(N) active#(U112(tt(),L,N)) -> U113#(isNat(N),L,N) active#(U112(tt(),L,N)) -> mark#(U113(isNat(N),L,N)) active#(U113(tt(),L,N)) -> isNatKind#(N) active#(U113(tt(),L,N)) -> U114#(isNatKind(N),L) active#(U113(tt(),L,N)) -> mark#(U114(isNatKind(N),L)) active#(U114(tt(),L)) -> length#(L) active#(U114(tt(),L)) -> s#(length(L)) active#(U114(tt(),L)) -> mark#(s(length(L))) active#(U12(tt(),V1)) -> isNatList#(V1) active#(U12(tt(),V1)) -> U13#(isNatList(V1)) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) active#(U121(tt(),IL)) -> isNatIListKind#(IL) active#(U121(tt(),IL)) -> U122#(isNatIListKind(IL)) active#(U121(tt(),IL)) -> mark#(U122(isNatIListKind(IL))) active#(U122(tt())) -> mark#(nil()) active#(U13(tt())) -> mark#(tt()) active#(U131(tt(),IL,M,N)) -> isNatIListKind#(IL) active#(U131(tt(),IL,M,N)) -> U132#(isNatIListKind(IL),IL,M,N) active#(U131(tt(),IL,M,N)) -> mark#(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#(U132(tt(),IL,M,N)) -> mark#(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#(U133(tt(),IL,M,N)) -> mark#(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#(U134(tt(),IL,M,N)) -> mark#(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#(U135(tt(),IL,M,N)) -> mark#(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#(U136(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) active#(U21(tt(),V1)) -> isNatKind#(V1) active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> isNat#(V1) active#(U22(tt(),V1)) -> U23#(isNat(V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) active#(U31(tt(),V)) -> isNatIListKind#(V) active#(U31(tt(),V)) -> U32#(isNatIListKind(V),V) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) active#(U32(tt(),V)) -> isNatList#(V) active#(U32(tt(),V)) -> U33#(isNatList(V)) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) active#(U33(tt())) -> mark#(tt()) active#(U41(tt(),V1,V2)) -> isNatKind#(V1) active#(U41(tt(),V1,V2)) -> U42#(isNatKind(V1),V1,V2) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) active#(U42(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U42(tt(),V1,V2)) -> U43#(isNatIListKind(V2),V1,V2) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) active#(U43(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U43(tt(),V1,V2)) -> U44#(isNatIListKind(V2),V1,V2) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) active#(U44(tt(),V1,V2)) -> isNat#(V1) active#(U44(tt(),V1,V2)) -> U45#(isNat(V1),V2) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) active#(U45(tt(),V2)) -> isNatIList#(V2) active#(U45(tt(),V2)) -> U46#(isNatIList(V2)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) active#(U46(tt())) -> mark#(tt()) active#(U51(tt(),V2)) -> isNatIListKind#(V2) active#(U51(tt(),V2)) -> U52#(isNatIListKind(V2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) active#(U52(tt())) -> mark#(tt()) active#(U61(tt(),V2)) -> isNatIListKind#(V2) active#(U61(tt(),V2)) -> U62#(isNatIListKind(V2)) 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)) -> isNatKind#(V1) active#(U91(tt(),V1,V2)) -> U92#(isNatKind(V1),V1,V2) active#(U91(tt(),V1,V2)) -> mark#(U92(isNatKind(V1),V1,V2)) active#(U92(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U92(tt(),V1,V2)) -> U93#(isNatIListKind(V2),V1,V2) active#(U92(tt(),V1,V2)) -> mark#(U93(isNatIListKind(V2),V1,V2)) active#(U93(tt(),V1,V2)) -> isNatIListKind#(V2) active#(U93(tt(),V1,V2)) -> U94#(isNatIListKind(V2),V1,V2) active#(U93(tt(),V1,V2)) -> mark#(U94(isNatIListKind(V2),V1,V2)) active#(U94(tt(),V1,V2)) -> isNat#(V1) active#(U94(tt(),V1,V2)) -> U95#(isNat(V1),V2) active#(U94(tt(),V1,V2)) -> mark#(U95(isNat(V1),V2)) active#(U95(tt(),V2)) -> isNatList#(V2) active#(U95(tt(),V2)) -> U96#(isNatList(V2)) active#(U95(tt(),V2)) -> mark#(U96(isNatList(V2))) active#(U96(tt())) -> mark#(tt()) active#(isNat(0())) -> mark#(tt()) active#(isNat(length(V1))) -> isNatIListKind#(V1) active#(isNat(length(V1))) -> U11#(isNatIListKind(V1),V1) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) active#(isNat(s(V1))) -> isNatKind#(V1) active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) active#(isNatIList(V)) -> isNatIListKind#(V) active#(isNatIList(V)) -> U31#(isNatIListKind(V),V) active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V)) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(V1,V2))) -> isNatKind#(V1) active#(isNatIList(cons(V1,V2))) -> U41#(isNatKind(V1),V1,V2) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) active#(isNatIListKind(nil())) -> mark#(tt()) active#(isNatIListKind(zeros())) -> mark#(tt()) active#(isNatIListKind(cons(V1,V2))) -> isNatKind#(V1) active#(isNatIListKind(cons(V1,V2))) -> U51#(isNatKind(V1),V2) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) active#(isNatIListKind(take(V1,V2))) -> isNatKind#(V1) active#(isNatIListKind(take(V1,V2))) -> U61#(isNatKind(V1),V2) active#(isNatIListKind(take(V1,V2))) -> mark#(U61(isNatKind(V1),V2)) active#(isNatKind(0())) -> mark#(tt()) active#(isNatKind(length(V1))) -> isNatIListKind#(V1) active#(isNatKind(length(V1))) -> U71#(isNatIListKind(V1)) active#(isNatKind(length(V1))) -> mark#(U71(isNatIListKind(V1))) active#(isNatKind(s(V1))) -> isNatKind#(V1) active#(isNatKind(s(V1))) -> U81#(isNatKind(V1)) active#(isNatKind(s(V1))) -> mark#(U81(isNatKind(V1))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(V1,V2))) -> isNatKind#(V1) active#(isNatList(cons(V1,V2))) -> U91#(isNatKind(V1),V1,V2) active#(isNatList(cons(V1,V2))) -> mark#(U91(isNatKind(V1),V1,V2)) active#(isNatList(take(V1,V2))) -> isNatKind#(V1) active#(isNatList(take(V1,V2))) -> U101#(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))) -> isNatList#(L) active#(length(cons(N,L))) -> U111#(isNatList(L),L,N) active#(length(cons(N,L))) -> mark#(U111(isNatList(L),L,N)) active#(take(0(),IL)) -> isNatIList#(IL) active#(take(0(),IL)) -> U121#(isNatIList(IL),IL) active#(take(0(),IL)) -> mark#(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#(take(s(M),cons(N,IL))) -> mark#(U131(isNatIList(IL),IL,M,N)) mark#(zeros()) -> active#(zeros()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(0()) -> active#(0()) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U101(X1,X2,X3)) -> U101#(mark(X1),X2,X3) mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3)) mark#(tt()) -> active#(tt()) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> U102#(mark(X1),X2,X3) mark#(U102(X1,X2,X3)) -> active#(U102(mark(X1),X2,X3)) mark#(isNatKind(X)) -> active#(isNatKind(X)) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> U103#(mark(X1),X2,X3) mark#(U103(X1,X2,X3)) -> active#(U103(mark(X1),X2,X3)) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> U104#(mark(X1),X2,X3) mark#(U104(X1,X2,X3)) -> active#(U104(mark(X1),X2,X3)) mark#(U105(X1,X2)) -> mark#(X1) mark#(U105(X1,X2)) -> U105#(mark(X1),X2) mark#(U105(X1,X2)) -> active#(U105(mark(X1),X2)) mark#(isNat(X)) -> active#(isNat(X)) mark#(U106(X)) -> mark#(X) mark#(U106(X)) -> U106#(mark(X)) mark#(U106(X)) -> active#(U106(mark(X))) mark#(isNatIList(X)) -> active#(isNatIList(X)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> U12#(mark(X1),X2) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) mark#(U111(X1,X2,X3)) -> mark#(X1) mark#(U111(X1,X2,X3)) -> U111#(mark(X1),X2,X3) mark#(U111(X1,X2,X3)) -> active#(U111(mark(X1),X2,X3)) mark#(U112(X1,X2,X3)) -> mark#(X1) mark#(U112(X1,X2,X3)) -> U112#(mark(X1),X2,X3) mark#(U112(X1,X2,X3)) -> active#(U112(mark(X1),X2,X3)) mark#(U113(X1,X2,X3)) -> mark#(X1) mark#(U113(X1,X2,X3)) -> U113#(mark(X1),X2,X3) mark#(U113(X1,X2,X3)) -> active#(U113(mark(X1),X2,X3)) mark#(U114(X1,X2)) -> mark#(X1) mark#(U114(X1,X2)) -> U114#(mark(X1),X2) mark#(U114(X1,X2)) -> active#(U114(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(length(X)) -> mark#(X) mark#(length(X)) -> length#(mark(X)) mark#(length(X)) -> active#(length(mark(X))) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> U13#(mark(X)) mark#(U13(X)) -> active#(U13(mark(X))) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(U121(X1,X2)) -> mark#(X1) mark#(U121(X1,X2)) -> U121#(mark(X1),X2) mark#(U121(X1,X2)) -> active#(U121(mark(X1),X2)) mark#(U122(X)) -> mark#(X) mark#(U122(X)) -> U122#(mark(X)) mark#(U122(X)) -> active#(U122(mark(X))) mark#(nil()) -> active#(nil()) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> U131#(mark(X1),X2,X3,X4) mark#(U131(X1,X2,X3,X4)) -> active#(U131(mark(X1),X2,X3,X4)) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> U132#(mark(X1),X2,X3,X4) mark#(U132(X1,X2,X3,X4)) -> active#(U132(mark(X1),X2,X3,X4)) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> U133#(mark(X1),X2,X3,X4) mark#(U133(X1,X2,X3,X4)) -> active#(U133(mark(X1),X2,X3,X4)) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> U134#(mark(X1),X2,X3,X4) mark#(U134(X1,X2,X3,X4)) -> active#(U134(mark(X1),X2,X3,X4)) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> U135#(mark(X1),X2,X3,X4) mark#(U135(X1,X2,X3,X4)) -> active#(U135(mark(X1),X2,X3,X4)) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> U136#(mark(X1),X2,X3,X4) mark#(U136(X1,X2,X3,X4)) -> active#(U136(mark(X1),X2,X3,X4)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> U21#(mark(X1),X2) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> U22#(mark(X1),X2) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> U23#(mark(X)) mark#(U23(X)) -> active#(U23(mark(X))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> U32#(mark(X1),X2) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> U33#(mark(X)) mark#(U33(X)) -> active#(U33(mark(X))) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> U42#(mark(X1),X2,X3) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> U43#(mark(X1),X2,X3) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> U44#(mark(X1),X2,X3) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> U45#(mark(X1),X2) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> U46#(mark(X)) mark#(U46(X)) -> active#(U46(mark(X))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> U52#(mark(X)) mark#(U52(X)) -> active#(U52(mark(X))) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> U71#(mark(X)) mark#(U71(X)) -> active#(U71(mark(X))) mark#(U81(X)) -> mark#(X) mark#(U81(X)) -> U81#(mark(X)) mark#(U81(X)) -> active#(U81(mark(X))) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> U91#(mark(X1),X2,X3) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> U92#(mark(X1),X2,X3) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> U93#(mark(X1),X2,X3) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> U94#(mark(X1),X2,X3) mark#(U94(X1,X2,X3)) -> active#(U94(mark(X1),X2,X3)) mark#(U95(X1,X2)) -> mark#(X1) mark#(U95(X1,X2)) -> U95#(mark(X1),X2) mark#(U95(X1,X2)) -> active#(U95(mark(X1),X2)) mark#(U96(X)) -> mark#(X) mark#(U96(X)) -> U96#(mark(X)) mark#(U96(X)) -> active#(U96(mark(X))) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3) U101#(active(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,active(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3) U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,mark(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,mark(X3)) -> U102#(X1,X2,X3) U102#(active(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,active(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,active(X3)) -> U102#(X1,X2,X3) isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,mark(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,mark(X3)) -> U103#(X1,X2,X3) U103#(active(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,active(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,active(X3)) -> U103#(X1,X2,X3) isNatIListKind#(mark(X)) -> isNatIListKind#(X) isNatIListKind#(active(X)) -> isNatIListKind#(X) U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,mark(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,mark(X3)) -> U104#(X1,X2,X3) U104#(active(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,active(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,active(X3)) -> U104#(X1,X2,X3) U105#(mark(X1),X2) -> U105#(X1,X2) U105#(X1,mark(X2)) -> U105#(X1,X2) U105#(active(X1),X2) -> U105#(X1,X2) U105#(X1,active(X2)) -> U105#(X1,X2) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) U106#(mark(X)) -> U106#(X) U106#(active(X)) -> U106#(X) isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) U111#(mark(X1),X2,X3) -> U111#(X1,X2,X3) U111#(X1,mark(X2),X3) -> U111#(X1,X2,X3) U111#(X1,X2,mark(X3)) -> U111#(X1,X2,X3) U111#(active(X1),X2,X3) -> U111#(X1,X2,X3) U111#(X1,active(X2),X3) -> U111#(X1,X2,X3) U111#(X1,X2,active(X3)) -> U111#(X1,X2,X3) U112#(mark(X1),X2,X3) -> U112#(X1,X2,X3) U112#(X1,mark(X2),X3) -> U112#(X1,X2,X3) U112#(X1,X2,mark(X3)) -> U112#(X1,X2,X3) U112#(active(X1),X2,X3) -> U112#(X1,X2,X3) U112#(X1,active(X2),X3) -> U112#(X1,X2,X3) U112#(X1,X2,active(X3)) -> U112#(X1,X2,X3) U113#(mark(X1),X2,X3) -> U113#(X1,X2,X3) U113#(X1,mark(X2),X3) -> U113#(X1,X2,X3) U113#(X1,X2,mark(X3)) -> U113#(X1,X2,X3) U113#(active(X1),X2,X3) -> U113#(X1,X2,X3) U113#(X1,active(X2),X3) -> U113#(X1,X2,X3) U113#(X1,X2,active(X3)) -> U113#(X1,X2,X3) U114#(mark(X1),X2) -> U114#(X1,X2) U114#(X1,mark(X2)) -> U114#(X1,X2) U114#(active(X1),X2) -> U114#(X1,X2) U114#(X1,active(X2)) -> U114#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) U13#(mark(X)) -> U13#(X) U13#(active(X)) -> U13#(X) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) U121#(mark(X1),X2) -> U121#(X1,X2) U121#(X1,mark(X2)) -> U121#(X1,X2) U121#(active(X1),X2) -> U121#(X1,X2) U121#(X1,active(X2)) -> U121#(X1,X2) U122#(mark(X)) -> U122#(X) U122#(active(X)) -> U122#(X) U131#(mark(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,mark(X2),X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,mark(X3),X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,X3,mark(X4)) -> U131#(X1,X2,X3,X4) U131#(active(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,active(X2),X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,active(X3),X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,X3,active(X4)) -> U131#(X1,X2,X3,X4) U132#(mark(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,mark(X2),X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,mark(X3),X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,X3,mark(X4)) -> U132#(X1,X2,X3,X4) U132#(active(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,active(X2),X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,active(X3),X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,X3,active(X4)) -> U132#(X1,X2,X3,X4) U133#(mark(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,mark(X2),X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,mark(X3),X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,X3,mark(X4)) -> U133#(X1,X2,X3,X4) U133#(active(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,active(X2),X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,active(X3),X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,X3,active(X4)) -> U133#(X1,X2,X3,X4) U134#(mark(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,mark(X2),X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,mark(X3),X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,X3,mark(X4)) -> U134#(X1,X2,X3,X4) U134#(active(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,active(X2),X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,active(X3),X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,X3,active(X4)) -> U134#(X1,X2,X3,X4) U135#(mark(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,mark(X2),X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,mark(X3),X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,X3,mark(X4)) -> U135#(X1,X2,X3,X4) U135#(active(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,active(X2),X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,active(X3),X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,X3,active(X4)) -> U135#(X1,X2,X3,X4) U136#(mark(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,mark(X2),X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,mark(X3),X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,X3,mark(X4)) -> U136#(X1,X2,X3,X4) U136#(active(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,active(X2),X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,active(X3),X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,X3,active(X4)) -> U136#(X1,X2,X3,X4) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) U21#(mark(X1),X2) -> U21#(X1,X2) U21#(X1,mark(X2)) -> U21#(X1,X2) U21#(active(X1),X2) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) U32#(active(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) U33#(mark(X)) -> U33#(X) U33#(active(X)) -> U33#(X) U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) U45#(active(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) U46#(mark(X)) -> U46#(X) U46#(active(X)) -> U46#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X)) -> U71#(X) U71#(active(X)) -> U71#(X) U81#(mark(X)) -> U81#(X) U81#(active(X)) -> U81#(X) U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,mark(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3) U91#(active(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,active(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3) U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,mark(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3) U92#(active(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,active(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3) U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,mark(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3) U93#(active(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,active(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3) U94#(mark(X1),X2,X3) -> U94#(X1,X2,X3) U94#(X1,mark(X2),X3) -> U94#(X1,X2,X3) U94#(X1,X2,mark(X3)) -> U94#(X1,X2,X3) U94#(active(X1),X2,X3) -> U94#(X1,X2,X3) U94#(X1,active(X2),X3) -> U94#(X1,X2,X3) U94#(X1,X2,active(X3)) -> U94#(X1,X2,X3) U95#(mark(X1),X2) -> U95#(X1,X2) U95#(X1,mark(X2)) -> U95#(X1,X2) U95#(active(X1),X2) -> U95#(X1,X2) U95#(X1,active(X2)) -> U95#(X1,X2) U96#(mark(X)) -> U96#(X) U96#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) graph: ... SCC Processor: #sccs: 55 #rules: 408 #arcs: 29328/304704 DPs: mark#(U96(X)) -> mark#(X) mark#(zeros()) -> active#(zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(U101(tt(),V1,V2)) -> mark#(U102(isNatKind(V1),V1,V2)) mark#(0()) -> active#(0()) active#(U102(tt(),V1,V2)) -> mark#(U103(isNatIListKind(V2),V1,V2)) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3)) active#(U103(tt(),V1,V2)) -> mark#(U104(isNatIListKind(V2),V1,V2)) mark#(tt()) -> active#(tt()) active#(U104(tt(),V1,V2)) -> mark#(U105(isNat(V1),V2)) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> active#(U102(mark(X1),X2,X3)) active#(U105(tt(),V2)) -> mark#(U106(isNatIList(V2))) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U106(tt())) -> mark#(tt()) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> active#(U103(mark(X1),X2,X3)) active#(U11(tt(),V1)) -> mark#(U12(isNatIListKind(V1),V1)) mark#(isNatIListKind(X)) -> active#(isNatIListKind(X)) active#(U111(tt(),L,N)) -> mark#(U112(isNatIListKind(L),L,N)) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> active#(U104(mark(X1),X2,X3)) active#(U112(tt(),L,N)) -> mark#(U113(isNat(N),L,N)) mark#(U105(X1,X2)) -> mark#(X1) mark#(U105(X1,X2)) -> active#(U105(mark(X1),X2)) active#(U113(tt(),L,N)) -> mark#(U114(isNatKind(N),L)) mark#(isNat(X)) -> active#(isNat(X)) active#(U114(tt(),L)) -> mark#(s(length(L))) mark#(U106(X)) -> mark#(X) mark#(U106(X)) -> active#(U106(mark(X))) active#(U12(tt(),V1)) -> mark#(U13(isNatList(V1))) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(U121(tt(),IL)) -> mark#(U122(isNatIListKind(IL))) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U122(tt())) -> mark#(nil()) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(U13(tt())) -> mark#(tt()) mark#(U111(X1,X2,X3)) -> mark#(X1) mark#(U111(X1,X2,X3)) -> active#(U111(mark(X1),X2,X3)) active#(U131(tt(),IL,M,N)) -> mark#(U132(isNatIListKind(IL),IL,M,N)) mark#(U112(X1,X2,X3)) -> mark#(X1) mark#(U112(X1,X2,X3)) -> active#(U112(mark(X1),X2,X3)) active#(U132(tt(),IL,M,N)) -> mark#(U133(isNat(M),IL,M,N)) mark#(U113(X1,X2,X3)) -> mark#(X1) mark#(U113(X1,X2,X3)) -> active#(U113(mark(X1),X2,X3)) active#(U133(tt(),IL,M,N)) -> mark#(U134(isNatKind(M),IL,M,N)) mark#(U114(X1,X2)) -> mark#(X1) mark#(U114(X1,X2)) -> active#(U114(mark(X1),X2)) active#(U134(tt(),IL,M,N)) -> mark#(U135(isNat(N),IL,M,N)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(U135(tt(),IL,M,N)) -> mark#(U136(isNatKind(N),IL,M,N)) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(U136(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) mark#(U13(X)) -> mark#(X) mark#(U13(X)) -> active#(U13(mark(X))) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) mark#(isNatList(X)) -> active#(isNatList(X)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U121(X1,X2)) -> mark#(X1) mark#(U121(X1,X2)) -> active#(U121(mark(X1),X2)) active#(U23(tt())) -> mark#(tt()) mark#(U122(X)) -> mark#(X) mark#(U122(X)) -> active#(U122(mark(X))) active#(U31(tt(),V)) -> mark#(U32(isNatIListKind(V),V)) mark#(nil()) -> active#(nil()) active#(U32(tt(),V)) -> mark#(U33(isNatList(V))) mark#(U131(X1,X2,X3,X4)) -> mark#(X1) mark#(U131(X1,X2,X3,X4)) -> active#(U131(mark(X1),X2,X3,X4)) active#(U33(tt())) -> mark#(tt()) mark#(U132(X1,X2,X3,X4)) -> mark#(X1) mark#(U132(X1,X2,X3,X4)) -> active#(U132(mark(X1),X2,X3,X4)) active#(U41(tt(),V1,V2)) -> mark#(U42(isNatKind(V1),V1,V2)) mark#(U133(X1,X2,X3,X4)) -> mark#(X1) mark#(U133(X1,X2,X3,X4)) -> active#(U133(mark(X1),X2,X3,X4)) active#(U42(tt(),V1,V2)) -> mark#(U43(isNatIListKind(V2),V1,V2)) mark#(U134(X1,X2,X3,X4)) -> mark#(X1) mark#(U134(X1,X2,X3,X4)) -> active#(U134(mark(X1),X2,X3,X4)) active#(U43(tt(),V1,V2)) -> mark#(U44(isNatIListKind(V2),V1,V2)) mark#(U135(X1,X2,X3,X4)) -> mark#(X1) mark#(U135(X1,X2,X3,X4)) -> active#(U135(mark(X1),X2,X3,X4)) active#(U44(tt(),V1,V2)) -> mark#(U45(isNat(V1),V2)) mark#(U136(X1,X2,X3,X4)) -> mark#(X1) mark#(U136(X1,X2,X3,X4)) -> active#(U136(mark(X1),X2,X3,X4)) active#(U45(tt(),V2)) -> mark#(U46(isNatIList(V2))) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(U46(tt())) -> mark#(tt()) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U51(tt(),V2)) -> mark#(U52(isNatIListKind(V2))) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U52(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U61(tt(),V2)) -> mark#(U62(isNatIListKind(V2))) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U62(tt())) -> mark#(tt()) mark#(U32(X1,X2)) -> mark#(X1) mark#(U32(X1,X2)) -> active#(U32(mark(X1),X2)) active#(U71(tt())) -> mark#(tt()) mark#(U33(X)) -> mark#(X) mark#(U33(X)) -> active#(U33(mark(X))) active#(U81(tt())) -> mark#(tt()) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> active#(U41(mark(X1),X2,X3)) active#(U91(tt(),V1,V2)) -> mark#(U92(isNatKind(V1),V1,V2)) mark#(U42(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2,X3)) -> active#(U42(mark(X1),X2,X3)) active#(U92(tt(),V1,V2)) -> mark#(U93(isNatIListKind(V2),V1,V2)) mark#(U43(X1,X2,X3)) -> mark#(X1) mark#(U43(X1,X2,X3)) -> active#(U43(mark(X1),X2,X3)) active#(U93(tt(),V1,V2)) -> mark#(U94(isNatIListKind(V2),V1,V2)) mark#(U44(X1,X2,X3)) -> mark#(X1) mark#(U44(X1,X2,X3)) -> active#(U44(mark(X1),X2,X3)) active#(U94(tt(),V1,V2)) -> mark#(U95(isNat(V1),V2)) mark#(U45(X1,X2)) -> mark#(X1) mark#(U45(X1,X2)) -> active#(U45(mark(X1),X2)) active#(U95(tt(),V2)) -> mark#(U96(isNatList(V2))) mark#(U46(X)) -> mark#(X) mark#(U46(X)) -> active#(U46(mark(X))) active#(U96(tt())) -> mark#(tt()) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(isNat(0())) -> mark#(tt()) mark#(U52(X)) -> mark#(X) mark#(U52(X)) -> active#(U52(mark(X))) active#(isNat(length(V1))) -> mark#(U11(isNatIListKind(V1),V1)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> active#(U62(mark(X))) active#(isNatIList(V)) -> mark#(U31(isNatIListKind(V),V)) mark#(U71(X)) -> mark#(X) mark#(U71(X)) -> active#(U71(mark(X))) active#(isNatIList(zeros())) -> mark#(tt()) mark#(U81(X)) -> mark#(X) mark#(U81(X)) -> active#(U81(mark(X))) active#(isNatIList(cons(V1,V2))) -> mark#(U41(isNatKind(V1),V1,V2)) mark#(U91(X1,X2,X3)) -> mark#(X1) mark#(U91(X1,X2,X3)) -> active#(U91(mark(X1),X2,X3)) active#(isNatIListKind(nil())) -> mark#(tt()) mark#(U92(X1,X2,X3)) -> mark#(X1) mark#(U92(X1,X2,X3)) -> active#(U92(mark(X1),X2,X3)) active#(isNatIListKind(zeros())) -> mark#(tt()) mark#(U93(X1,X2,X3)) -> mark#(X1) mark#(U93(X1,X2,X3)) -> active#(U93(mark(X1),X2,X3)) active#(isNatIListKind(cons(V1,V2))) -> mark#(U51(isNatKind(V1),V2)) mark#(U94(X1,X2,X3)) -> mark#(X1) mark#(U94(X1,X2,X3)) -> active#(U94(mark(X1),X2,X3)) active#(isNatIListKind(take(V1,V2))) -> mark#(U61(isNatKind(V1),V2)) mark#(U95(X1,X2)) -> mark#(X1) mark#(U95(X1,X2)) -> active#(U95(mark(X1),X2)) active#(isNatKind(0())) -> mark#(tt()) mark#(U96(X)) -> active#(U96(mark(X))) 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)) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,mark(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,mark(X3)) -> U102#(X1,X2,X3) U102#(active(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,active(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: isNatIListKind#(mark(X)) -> isNatIListKind#(X) isNatIListKind#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,mark(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,mark(X3)) -> U103#(X1,X2,X3) U103#(active(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,active(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,mark(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,mark(X3)) -> U104#(X1,X2,X3) U104#(active(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,active(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: isNat#(mark(X)) -> isNat#(X) isNat#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U105#(mark(X1),X2) -> U105#(X1,X2) U105#(X1,mark(X2)) -> U105#(X1,X2) U105#(active(X1),X2) -> U105#(X1,X2) U105#(X1,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U106#(mark(X)) -> U106#(X) U106#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U112#(mark(X1),X2,X3) -> U112#(X1,X2,X3) U112#(X1,mark(X2),X3) -> U112#(X1,X2,X3) U112#(X1,X2,mark(X3)) -> U112#(X1,X2,X3) U112#(active(X1),X2,X3) -> U112#(X1,X2,X3) U112#(X1,active(X2),X3) -> U112#(X1,X2,X3) U112#(X1,X2,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U113#(mark(X1),X2,X3) -> U113#(X1,X2,X3) U113#(X1,mark(X2),X3) -> U113#(X1,X2,X3) U113#(X1,X2,mark(X3)) -> U113#(X1,X2,X3) U113#(active(X1),X2,X3) -> U113#(X1,X2,X3) U113#(X1,active(X2),X3) -> U113#(X1,X2,X3) U113#(X1,X2,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U114#(mark(X1),X2) -> U114#(X1,X2) U114#(X1,mark(X2)) -> U114#(X1,X2) U114#(active(X1),X2) -> U114#(X1,X2) U114#(X1,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: length#(mark(X)) -> length#(X) length#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: s#(mark(X)) -> s#(X) s#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U13#(mark(X)) -> U13#(X) U13#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U122#(mark(X)) -> U122#(X) U122#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U132#(mark(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,mark(X2),X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,mark(X3),X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,X3,mark(X4)) -> U132#(X1,X2,X3,X4) U132#(active(X1),X2,X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,active(X2),X3,X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,active(X3),X4) -> U132#(X1,X2,X3,X4) U132#(X1,X2,X3,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U133#(mark(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,mark(X2),X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,mark(X3),X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,X3,mark(X4)) -> U133#(X1,X2,X3,X4) U133#(active(X1),X2,X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,active(X2),X3,X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,active(X3),X4) -> U133#(X1,X2,X3,X4) U133#(X1,X2,X3,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U134#(mark(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,mark(X2),X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,mark(X3),X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,X3,mark(X4)) -> U134#(X1,X2,X3,X4) U134#(active(X1),X2,X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,active(X2),X3,X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,active(X3),X4) -> U134#(X1,X2,X3,X4) U134#(X1,X2,X3,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U135#(mark(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,mark(X2),X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,mark(X3),X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,X3,mark(X4)) -> U135#(X1,X2,X3,X4) U135#(active(X1),X2,X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,active(X2),X3,X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,active(X3),X4) -> U135#(X1,X2,X3,X4) U135#(X1,X2,X3,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U136#(mark(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,mark(X2),X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,mark(X3),X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,X3,mark(X4)) -> U136#(X1,X2,X3,X4) U136#(active(X1),X2,X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,active(X2),X3,X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,active(X3),X4) -> U136#(X1,X2,X3,X4) U136#(X1,X2,X3,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U23#(mark(X)) -> U23#(X) U23#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U32#(mark(X1),X2) -> U32#(X1,X2) U32#(X1,mark(X2)) -> U32#(X1,X2) U32#(active(X1),X2) -> U32#(X1,X2) U32#(X1,active(X2)) -> U32#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U33#(mark(X)) -> U33#(X) U33#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U42#(mark(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,mark(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,mark(X3)) -> U42#(X1,X2,X3) U42#(active(X1),X2,X3) -> U42#(X1,X2,X3) U42#(X1,active(X2),X3) -> U42#(X1,X2,X3) U42#(X1,X2,active(X3)) -> U42#(X1,X2,X3) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U43#(mark(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,mark(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,mark(X3)) -> U43#(X1,X2,X3) U43#(active(X1),X2,X3) -> U43#(X1,X2,X3) U43#(X1,active(X2),X3) -> U43#(X1,X2,X3) U43#(X1,X2,active(X3)) -> U43#(X1,X2,X3) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U44#(mark(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,mark(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,mark(X3)) -> U44#(X1,X2,X3) U44#(active(X1),X2,X3) -> U44#(X1,X2,X3) U44#(X1,active(X2),X3) -> U44#(X1,X2,X3) U44#(X1,X2,active(X3)) -> U44#(X1,X2,X3) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U45#(mark(X1),X2) -> U45#(X1,X2) U45#(X1,mark(X2)) -> U45#(X1,X2) U45#(active(X1),X2) -> U45#(X1,X2) U45#(X1,active(X2)) -> U45#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U46#(mark(X)) -> U46#(X) U46#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U52#(mark(X)) -> U52#(X) U52#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U62#(mark(X)) -> U62#(X) U62#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U92#(mark(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,mark(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,mark(X3)) -> U92#(X1,X2,X3) U92#(active(X1),X2,X3) -> U92#(X1,X2,X3) U92#(X1,active(X2),X3) -> U92#(X1,X2,X3) U92#(X1,X2,active(X3)) -> U92#(X1,X2,X3) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U93#(mark(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,mark(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,mark(X3)) -> U93#(X1,X2,X3) U93#(active(X1),X2,X3) -> U93#(X1,X2,X3) U93#(X1,active(X2),X3) -> U93#(X1,X2,X3) U93#(X1,X2,active(X3)) -> U93#(X1,X2,X3) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U94#(mark(X1),X2,X3) -> U94#(X1,X2,X3) U94#(X1,mark(X2),X3) -> U94#(X1,X2,X3) U94#(X1,X2,mark(X3)) -> U94#(X1,X2,X3) U94#(active(X1),X2,X3) -> U94#(X1,X2,X3) U94#(X1,active(X2),X3) -> U94#(X1,X2,X3) U94#(X1,X2,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U95#(mark(X1),X2) -> U95#(X1,X2) U95#(X1,mark(X2)) -> U95#(X1,X2) U95#(active(X1),X2) -> U95#(X1,X2) U95#(X1,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U96#(mark(X)) -> U96#(X) U96#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U21#(mark(X1),X2) -> U21#(X1,X2) U21#(X1,mark(X2)) -> U21#(X1,X2) U21#(active(X1),X2) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U41#(mark(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,mark(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,mark(X3)) -> U41#(X1,X2,X3) U41#(active(X1),X2,X3) -> U41#(X1,X2,X3) U41#(X1,active(X2),X3) -> U41#(X1,X2,X3) U41#(X1,X2,active(X3)) -> U41#(X1,X2,X3) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U71#(mark(X)) -> U71#(X) U71#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U81#(mark(X)) -> U81#(X) U81#(active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U91#(mark(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,mark(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,mark(X3)) -> U91#(X1,X2,X3) U91#(active(X1),X2,X3) -> U91#(X1,X2,X3) U91#(X1,active(X2),X3) -> U91#(X1,X2,X3) U91#(X1,X2,active(X3)) -> U91#(X1,X2,X3) 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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3) U101#(active(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,active(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U111#(mark(X1),X2,X3) -> U111#(X1,X2,X3) U111#(X1,mark(X2),X3) -> U111#(X1,X2,X3) U111#(X1,X2,mark(X3)) -> U111#(X1,X2,X3) U111#(active(X1),X2,X3) -> U111#(X1,X2,X3) U111#(X1,active(X2),X3) -> U111#(X1,X2,X3) U111#(X1,X2,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U121#(mark(X1),X2) -> U121#(X1,X2) U121#(X1,mark(X2)) -> U121#(X1,X2) U121#(active(X1),X2) -> U121#(X1,X2) U121#(X1,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open DPs: U131#(mark(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,mark(X2),X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,mark(X3),X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,X3,mark(X4)) -> U131#(X1,X2,X3,X4) U131#(active(X1),X2,X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,active(X2),X3,X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,active(X3),X4) -> U131#(X1,X2,X3,X4) U131#(X1,X2,X3,active(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)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNatIListKind(X)) -> active(isNatIListKind(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(U105(X1,X2)) -> active(U105(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(U106(X)) -> active(U106(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(U111(X1,X2,X3)) -> active(U111(mark(X1),X2,X3)) mark(U112(X1,X2,X3)) -> active(U112(mark(X1),X2,X3)) mark(U113(X1,X2,X3)) -> active(U113(mark(X1),X2,X3)) mark(U114(X1,X2)) -> active(U114(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U13(X)) -> active(U13(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U121(X1,X2)) -> active(U121(mark(X1),X2)) mark(U122(X)) -> active(U122(mark(X))) mark(nil()) -> active(nil()) mark(U131(X1,X2,X3,X4)) -> active(U131(mark(X1),X2,X3,X4)) mark(U132(X1,X2,X3,X4)) -> active(U132(mark(X1),X2,X3,X4)) mark(U133(X1,X2,X3,X4)) -> active(U133(mark(X1),X2,X3,X4)) mark(U134(X1,X2,X3,X4)) -> active(U134(mark(X1),X2,X3,X4)) mark(U135(X1,X2,X3,X4)) -> active(U135(mark(X1),X2,X3,X4)) mark(U136(X1,X2,X3,X4)) -> active(U136(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2)) -> active(U31(mark(X1),X2)) mark(U32(X1,X2)) -> active(U32(mark(X1),X2)) mark(U33(X)) -> active(U33(mark(X))) mark(U41(X1,X2,X3)) -> active(U41(mark(X1),X2,X3)) mark(U42(X1,X2,X3)) -> active(U42(mark(X1),X2,X3)) mark(U43(X1,X2,X3)) -> active(U43(mark(X1),X2,X3)) mark(U44(X1,X2,X3)) -> active(U44(mark(X1),X2,X3)) mark(U45(X1,X2)) -> active(U45(mark(X1),X2)) mark(U46(X)) -> active(U46(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X)) -> active(U71(mark(X))) mark(U81(X)) -> active(U81(mark(X))) mark(U91(X1,X2,X3)) -> active(U91(mark(X1),X2,X3)) mark(U92(X1,X2,X3)) -> active(U92(mark(X1),X2,X3)) mark(U93(X1,X2,X3)) -> active(U93(mark(X1),X2,X3)) mark(U94(X1,X2,X3)) -> active(U94(mark(X1),X2,X3)) mark(U95(X1,X2)) -> active(U95(mark(X1),X2)) mark(U96(X)) -> active(U96(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNatIListKind(mark(X)) -> isNatIListKind(X) isNatIListKind(active(X)) -> isNatIListKind(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) U105(mark(X1),X2) -> U105(X1,X2) U105(X1,mark(X2)) -> U105(X1,X2) U105(active(X1),X2) -> U105(X1,X2) U105(X1,active(X2)) -> U105(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U106(mark(X)) -> U106(X) U106(active(X)) -> U106(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) U111(mark(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,mark(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,mark(X3)) -> U111(X1,X2,X3) U111(active(X1),X2,X3) -> U111(X1,X2,X3) U111(X1,active(X2),X3) -> U111(X1,X2,X3) U111(X1,X2,active(X3)) -> U111(X1,X2,X3) U112(mark(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,mark(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,mark(X3)) -> U112(X1,X2,X3) U112(active(X1),X2,X3) -> U112(X1,X2,X3) U112(X1,active(X2),X3) -> U112(X1,X2,X3) U112(X1,X2,active(X3)) -> U112(X1,X2,X3) U113(mark(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,mark(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,mark(X3)) -> U113(X1,X2,X3) U113(active(X1),X2,X3) -> U113(X1,X2,X3) U113(X1,active(X2),X3) -> U113(X1,X2,X3) U113(X1,X2,active(X3)) -> U113(X1,X2,X3) U114(mark(X1),X2) -> U114(X1,X2) U114(X1,mark(X2)) -> U114(X1,X2) U114(active(X1),X2) -> U114(X1,X2) U114(X1,active(X2)) -> U114(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U13(mark(X)) -> U13(X) U13(active(X)) -> U13(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U121(mark(X1),X2) -> U121(X1,X2) U121(X1,mark(X2)) -> U121(X1,X2) U121(active(X1),X2) -> U121(X1,X2) U121(X1,active(X2)) -> U121(X1,X2) U122(mark(X)) -> U122(X) U122(active(X)) -> U122(X) U131(mark(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,mark(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,mark(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,mark(X4)) -> U131(X1,X2,X3,X4) U131(active(X1),X2,X3,X4) -> U131(X1,X2,X3,X4) U131(X1,active(X2),X3,X4) -> U131(X1,X2,X3,X4) U131(X1,X2,active(X3),X4) -> U131(X1,X2,X3,X4) U131(X1,X2,X3,active(X4)) -> U131(X1,X2,X3,X4) U132(mark(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,mark(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,mark(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,mark(X4)) -> U132(X1,X2,X3,X4) U132(active(X1),X2,X3,X4) -> U132(X1,X2,X3,X4) U132(X1,active(X2),X3,X4) -> U132(X1,X2,X3,X4) U132(X1,X2,active(X3),X4) -> U132(X1,X2,X3,X4) U132(X1,X2,X3,active(X4)) -> U132(X1,X2,X3,X4) U133(mark(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,mark(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,mark(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,mark(X4)) -> U133(X1,X2,X3,X4) U133(active(X1),X2,X3,X4) -> U133(X1,X2,X3,X4) U133(X1,active(X2),X3,X4) -> U133(X1,X2,X3,X4) U133(X1,X2,active(X3),X4) -> U133(X1,X2,X3,X4) U133(X1,X2,X3,active(X4)) -> U133(X1,X2,X3,X4) U134(mark(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,mark(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,mark(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,mark(X4)) -> U134(X1,X2,X3,X4) U134(active(X1),X2,X3,X4) -> U134(X1,X2,X3,X4) U134(X1,active(X2),X3,X4) -> U134(X1,X2,X3,X4) U134(X1,X2,active(X3),X4) -> U134(X1,X2,X3,X4) U134(X1,X2,X3,active(X4)) -> U134(X1,X2,X3,X4) U135(mark(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,mark(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,mark(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,mark(X4)) -> U135(X1,X2,X3,X4) U135(active(X1),X2,X3,X4) -> U135(X1,X2,X3,X4) U135(X1,active(X2),X3,X4) -> U135(X1,X2,X3,X4) U135(X1,X2,active(X3),X4) -> U135(X1,X2,X3,X4) U135(X1,X2,X3,active(X4)) -> U135(X1,X2,X3,X4) U136(mark(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,mark(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,mark(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,mark(X4)) -> U136(X1,X2,X3,X4) U136(active(X1),X2,X3,X4) -> U136(X1,X2,X3,X4) U136(X1,active(X2),X3,X4) -> U136(X1,X2,X3,X4) U136(X1,X2,active(X3),X4) -> U136(X1,X2,X3,X4) U136(X1,X2,X3,active(X4)) -> U136(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X1),X2) -> U32(X1,X2) U32(X1,mark(X2)) -> U32(X1,X2) U32(active(X1),X2) -> U32(X1,X2) U32(X1,active(X2)) -> U32(X1,X2) U33(mark(X)) -> U33(X) U33(active(X)) -> U33(X) U41(mark(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,mark(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,mark(X3)) -> U41(X1,X2,X3) U41(active(X1),X2,X3) -> U41(X1,X2,X3) U41(X1,active(X2),X3) -> U41(X1,X2,X3) U41(X1,X2,active(X3)) -> U41(X1,X2,X3) U42(mark(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,mark(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,mark(X3)) -> U42(X1,X2,X3) U42(active(X1),X2,X3) -> U42(X1,X2,X3) U42(X1,active(X2),X3) -> U42(X1,X2,X3) U42(X1,X2,active(X3)) -> U42(X1,X2,X3) U43(mark(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,mark(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,mark(X3)) -> U43(X1,X2,X3) U43(active(X1),X2,X3) -> U43(X1,X2,X3) U43(X1,active(X2),X3) -> U43(X1,X2,X3) U43(X1,X2,active(X3)) -> U43(X1,X2,X3) U44(mark(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,mark(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,mark(X3)) -> U44(X1,X2,X3) U44(active(X1),X2,X3) -> U44(X1,X2,X3) U44(X1,active(X2),X3) -> U44(X1,X2,X3) U44(X1,X2,active(X3)) -> U44(X1,X2,X3) U45(mark(X1),X2) -> U45(X1,X2) U45(X1,mark(X2)) -> U45(X1,X2) U45(active(X1),X2) -> U45(X1,X2) U45(X1,active(X2)) -> U45(X1,X2) U46(mark(X)) -> U46(X) U46(active(X)) -> U46(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X)) -> U71(X) U71(active(X)) -> U71(X) U81(mark(X)) -> U81(X) U81(active(X)) -> U81(X) U91(mark(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,mark(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,mark(X3)) -> U91(X1,X2,X3) U91(active(X1),X2,X3) -> U91(X1,X2,X3) U91(X1,active(X2),X3) -> U91(X1,X2,X3) U91(X1,X2,active(X3)) -> U91(X1,X2,X3) U92(mark(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,mark(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,mark(X3)) -> U92(X1,X2,X3) U92(active(X1),X2,X3) -> U92(X1,X2,X3) U92(X1,active(X2),X3) -> U92(X1,X2,X3) U92(X1,X2,active(X3)) -> U92(X1,X2,X3) U93(mark(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,mark(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,mark(X3)) -> U93(X1,X2,X3) U93(active(X1),X2,X3) -> U93(X1,X2,X3) U93(X1,active(X2),X3) -> U93(X1,X2,X3) U93(X1,X2,active(X3)) -> U93(X1,X2,X3) U94(mark(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,mark(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,mark(X3)) -> U94(X1,X2,X3) U94(active(X1),X2,X3) -> U94(X1,X2,X3) U94(X1,active(X2),X3) -> U94(X1,X2,X3) U94(X1,X2,active(X3)) -> U94(X1,X2,X3) U95(mark(X1),X2) -> U95(X1,X2) U95(X1,mark(X2)) -> U95(X1,X2) U95(active(X1),X2) -> U95(X1,X2) U95(X1,active(X2)) -> U95(X1,X2) U96(mark(X)) -> U96(X) U96(active(X)) -> U96(X) Open