0 QTRS
↳1 DependencyPairsProof (⇔)
↳2 QDP
↳3 DependencyGraphProof (⇔)
↳4 AND
↳5 QDP
↳6 QDPOrderProof (⇔)
↳7 QDP
↳8 PisEmptyProof (⇔)
↳9 TRUE
↳10 QDP
↳11 QDPOrderProof (⇔)
↳12 QDP
↳13 QDPOrderProof (⇔)
↳14 QDP
↳15 QDPOrderProof (⇔)
↳16 QDP
↳17 QDPOrderProof (⇔)
↳18 QDP
↳19 QDPOrderProof (⇔)
↳20 QDP
↳21 PisEmptyProof (⇔)
↳22 TRUE
↳23 QDP
↳24 QDPOrderProof (⇔)
↳25 QDP
↳26 QDPOrderProof (⇔)
↳27 QDP
↳28 PisEmptyProof (⇔)
↳29 TRUE
↳30 QDP
↳31 QDPOrderProof (⇔)
↳32 QDP
↳33 PisEmptyProof (⇔)
↳34 TRUE
↳35 QDP
↳36 QDPOrderProof (⇔)
↳37 QDP
↳38 PisEmptyProof (⇔)
↳39 TRUE
↳40 QDP
↳41 QDPOrderProof (⇔)
↳42 QDP
↳43 PisEmptyProof (⇔)
↳44 TRUE
↳45 QDP
↳46 QDPOrderProof (⇔)
↳47 QDP
↳48 PisEmptyProof (⇔)
↳49 TRUE
↳50 QDP
↳51 QDPOrderProof (⇔)
↳52 QDP
↳53 PisEmptyProof (⇔)
↳54 TRUE
↳55 QDP
↳56 QDPOrderProof (⇔)
↳57 QDP
↳58 QDPOrderProof (⇔)
↳59 QDP
↳60 QDPOrderProof (⇔)
↳61 QDP
↳62 PisEmptyProof (⇔)
↳63 TRUE
↳64 QDP
↳65 QDPOrderProof (⇔)
↳66 QDP
↳67 QDPOrderProof (⇔)
↳68 QDP
↳69 QDPOrderProof (⇔)
↳70 QDP
↳71 PisEmptyProof (⇔)
↳72 TRUE
↳73 QDP
↳74 QDPOrderProof (⇔)
↳75 QDP
↳76 PisEmptyProof (⇔)
↳77 TRUE
↳78 QDP
↳79 QDPOrderProof (⇔)
↳80 QDP
↳81 QDPOrderProof (⇔)
↳82 QDP
↳83 QDPOrderProof (⇔)
↳84 QDP
↳85 PisEmptyProof (⇔)
↳86 TRUE
↳87 QDP
↳88 QDPOrderProof (⇔)
↳89 QDP
↳90 PisEmptyProof (⇔)
↳91 TRUE
↳92 QDP
↳93 QDPOrderProof (⇔)
↳94 QDP
↳95 PisEmptyProof (⇔)
↳96 TRUE
↳97 QDP
↳98 QDPOrderProof (⇔)
↳99 QDP
↳100 QDPOrderProof (⇔)
↳101 QDP
↳102 QDPOrderProof (⇔)
↳103 QDP
↳104 PisEmptyProof (⇔)
↳105 TRUE
↳106 QDP
↳107 QDPOrderProof (⇔)
↳108 QDP
↳109 PisEmptyProof (⇔)
↳110 TRUE
↳111 QDP
↳112 QDPOrderProof (⇔)
↳113 QDP
↳114 PisEmptyProof (⇔)
↳115 TRUE
↳116 QDP
↳117 QDPOrderProof (⇔)
↳118 QDP
↳119 PisEmptyProof (⇔)
↳120 TRUE
↳121 QDP
↳122 QDPOrderProof (⇔)
↳123 QDP
↳124 PisEmptyProof (⇔)
↳125 TRUE
↳126 QDP
↳127 QDPOrderProof (⇔)
↳128 QDP
↳129 PisEmptyProof (⇔)
↳130 TRUE
↳131 QDP
↳132 QDPOrderProof (⇔)
↳133 QDP
↳134 PisEmptyProof (⇔)
↳135 TRUE
↳136 QDP
↳137 QDPOrderProof (⇔)
↳138 QDP
↳139 QDPOrderProof (⇔)
↳140 QDP
↳141 QDPOrderProof (⇔)
↳142 QDP
↳143 PisEmptyProof (⇔)
↳144 TRUE
↳145 QDP
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
ACTIVE(zeros) → MARK(cons(0, zeros))
ACTIVE(zeros) → CONS(0, zeros)
ACTIVE(U11(tt)) → MARK(tt)
ACTIVE(U21(tt)) → MARK(tt)
ACTIVE(U31(tt)) → MARK(tt)
ACTIVE(U41(tt, V2)) → MARK(U42(isNatIList(V2)))
ACTIVE(U41(tt, V2)) → U421(isNatIList(V2))
ACTIVE(U41(tt, V2)) → ISNATILIST(V2)
ACTIVE(U42(tt)) → MARK(tt)
ACTIVE(U51(tt, V2)) → MARK(U52(isNatList(V2)))
ACTIVE(U51(tt, V2)) → U521(isNatList(V2))
ACTIVE(U51(tt, V2)) → ISNATLIST(V2)
ACTIVE(U52(tt)) → MARK(tt)
ACTIVE(U61(tt, V2)) → MARK(U62(isNatIList(V2)))
ACTIVE(U61(tt, V2)) → U621(isNatIList(V2))
ACTIVE(U61(tt, V2)) → ISNATILIST(V2)
ACTIVE(U62(tt)) → MARK(tt)
ACTIVE(U71(tt, L, N)) → MARK(U72(isNat(N), L))
ACTIVE(U71(tt, L, N)) → U721(isNat(N), L)
ACTIVE(U71(tt, L, N)) → ISNAT(N)
ACTIVE(U72(tt, L)) → MARK(s(length(L)))
ACTIVE(U72(tt, L)) → S(length(L))
ACTIVE(U72(tt, L)) → LENGTH(L)
ACTIVE(U81(tt)) → MARK(nil)
ACTIVE(U91(tt, IL, M, N)) → MARK(U92(isNat(M), IL, M, N))
ACTIVE(U91(tt, IL, M, N)) → U921(isNat(M), IL, M, N)
ACTIVE(U91(tt, IL, M, N)) → ISNAT(M)
ACTIVE(U92(tt, IL, M, N)) → MARK(U93(isNat(N), IL, M, N))
ACTIVE(U92(tt, IL, M, N)) → U931(isNat(N), IL, M, N)
ACTIVE(U92(tt, IL, M, N)) → ISNAT(N)
ACTIVE(U93(tt, IL, M, N)) → MARK(cons(N, take(M, IL)))
ACTIVE(U93(tt, IL, M, N)) → CONS(N, take(M, IL))
ACTIVE(U93(tt, IL, M, N)) → TAKE(M, IL)
ACTIVE(isNat(0)) → MARK(tt)
ACTIVE(isNat(length(V1))) → MARK(U11(isNatList(V1)))
ACTIVE(isNat(length(V1))) → U111(isNatList(V1))
ACTIVE(isNat(length(V1))) → ISNATLIST(V1)
ACTIVE(isNat(s(V1))) → MARK(U21(isNat(V1)))
ACTIVE(isNat(s(V1))) → U211(isNat(V1))
ACTIVE(isNat(s(V1))) → ISNAT(V1)
ACTIVE(isNatIList(V)) → MARK(U31(isNatList(V)))
ACTIVE(isNatIList(V)) → U311(isNatList(V))
ACTIVE(isNatIList(V)) → ISNATLIST(V)
ACTIVE(isNatIList(zeros)) → MARK(tt)
ACTIVE(isNatIList(cons(V1, V2))) → MARK(U41(isNat(V1), V2))
ACTIVE(isNatIList(cons(V1, V2))) → U411(isNat(V1), V2)
ACTIVE(isNatIList(cons(V1, V2))) → ISNAT(V1)
ACTIVE(isNatList(nil)) → MARK(tt)
ACTIVE(isNatList(cons(V1, V2))) → MARK(U51(isNat(V1), V2))
ACTIVE(isNatList(cons(V1, V2))) → U511(isNat(V1), V2)
ACTIVE(isNatList(cons(V1, V2))) → ISNAT(V1)
ACTIVE(isNatList(take(V1, V2))) → MARK(U61(isNat(V1), V2))
ACTIVE(isNatList(take(V1, V2))) → U611(isNat(V1), V2)
ACTIVE(isNatList(take(V1, V2))) → ISNAT(V1)
ACTIVE(length(nil)) → MARK(0)
ACTIVE(length(cons(N, L))) → MARK(U71(isNatList(L), L, N))
ACTIVE(length(cons(N, L))) → U711(isNatList(L), L, N)
ACTIVE(length(cons(N, L))) → ISNATLIST(L)
ACTIVE(take(0, IL)) → MARK(U81(isNatIList(IL)))
ACTIVE(take(0, IL)) → U811(isNatIList(IL))
ACTIVE(take(0, IL)) → ISNATILIST(IL)
ACTIVE(take(s(M), cons(N, IL))) → MARK(U91(isNatIList(IL), IL, M, N))
ACTIVE(take(s(M), cons(N, IL))) → U911(isNatIList(IL), IL, M, N)
ACTIVE(take(s(M), cons(N, IL))) → ISNATILIST(IL)
MARK(zeros) → ACTIVE(zeros)
MARK(cons(X1, X2)) → ACTIVE(cons(mark(X1), X2))
MARK(cons(X1, X2)) → CONS(mark(X1), X2)
MARK(cons(X1, X2)) → MARK(X1)
MARK(0) → ACTIVE(0)
MARK(U11(X)) → ACTIVE(U11(mark(X)))
MARK(U11(X)) → U111(mark(X))
MARK(U11(X)) → MARK(X)
MARK(tt) → ACTIVE(tt)
MARK(U21(X)) → ACTIVE(U21(mark(X)))
MARK(U21(X)) → U211(mark(X))
MARK(U21(X)) → MARK(X)
MARK(U31(X)) → ACTIVE(U31(mark(X)))
MARK(U31(X)) → U311(mark(X))
MARK(U31(X)) → MARK(X)
MARK(U41(X1, X2)) → ACTIVE(U41(mark(X1), X2))
MARK(U41(X1, X2)) → U411(mark(X1), X2)
MARK(U41(X1, X2)) → MARK(X1)
MARK(U42(X)) → ACTIVE(U42(mark(X)))
MARK(U42(X)) → U421(mark(X))
MARK(U42(X)) → MARK(X)
MARK(isNatIList(X)) → ACTIVE(isNatIList(X))
MARK(U51(X1, X2)) → ACTIVE(U51(mark(X1), X2))
MARK(U51(X1, X2)) → U511(mark(X1), X2)
MARK(U51(X1, X2)) → MARK(X1)
MARK(U52(X)) → ACTIVE(U52(mark(X)))
MARK(U52(X)) → U521(mark(X))
MARK(U52(X)) → MARK(X)
MARK(isNatList(X)) → ACTIVE(isNatList(X))
MARK(U61(X1, X2)) → ACTIVE(U61(mark(X1), X2))
MARK(U61(X1, X2)) → U611(mark(X1), X2)
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X)) → ACTIVE(U62(mark(X)))
MARK(U62(X)) → U621(mark(X))
MARK(U62(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → ACTIVE(U71(mark(X1), X2, X3))
MARK(U71(X1, X2, X3)) → U711(mark(X1), X2, X3)
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → ACTIVE(U72(mark(X1), X2))
MARK(U72(X1, X2)) → U721(mark(X1), X2)
MARK(U72(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
MARK(s(X)) → ACTIVE(s(mark(X)))
MARK(s(X)) → S(mark(X))
MARK(s(X)) → MARK(X)
MARK(length(X)) → ACTIVE(length(mark(X)))
MARK(length(X)) → LENGTH(mark(X))
MARK(length(X)) → MARK(X)
MARK(U81(X)) → ACTIVE(U81(mark(X)))
MARK(U81(X)) → U811(mark(X))
MARK(U81(X)) → MARK(X)
MARK(nil) → ACTIVE(nil)
MARK(U91(X1, X2, X3, X4)) → ACTIVE(U91(mark(X1), X2, X3, X4))
MARK(U91(X1, X2, X3, X4)) → U911(mark(X1), X2, X3, X4)
MARK(U91(X1, X2, X3, X4)) → MARK(X1)
MARK(U92(X1, X2, X3, X4)) → ACTIVE(U92(mark(X1), X2, X3, X4))
MARK(U92(X1, X2, X3, X4)) → U921(mark(X1), X2, X3, X4)
MARK(U92(X1, X2, X3, X4)) → MARK(X1)
MARK(U93(X1, X2, X3, X4)) → ACTIVE(U93(mark(X1), X2, X3, X4))
MARK(U93(X1, X2, X3, X4)) → U931(mark(X1), X2, X3, X4)
MARK(U93(X1, X2, X3, X4)) → MARK(X1)
MARK(take(X1, X2)) → ACTIVE(take(mark(X1), mark(X2)))
MARK(take(X1, X2)) → TAKE(mark(X1), mark(X2))
MARK(take(X1, X2)) → MARK(X1)
MARK(take(X1, X2)) → MARK(X2)
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)
U111(mark(X)) → U111(X)
U111(active(X)) → U111(X)
U211(mark(X)) → U211(X)
U211(active(X)) → U211(X)
U311(mark(X)) → U311(X)
U311(active(X)) → U311(X)
U411(mark(X1), X2) → U411(X1, X2)
U411(X1, mark(X2)) → U411(X1, X2)
U411(active(X1), X2) → U411(X1, X2)
U411(X1, active(X2)) → U411(X1, X2)
U421(mark(X)) → U421(X)
U421(active(X)) → U421(X)
ISNATILIST(mark(X)) → ISNATILIST(X)
ISNATILIST(active(X)) → ISNATILIST(X)
U511(mark(X1), X2) → U511(X1, X2)
U511(X1, mark(X2)) → U511(X1, X2)
U511(active(X1), X2) → U511(X1, X2)
U511(X1, active(X2)) → U511(X1, X2)
U521(mark(X)) → U521(X)
U521(active(X)) → U521(X)
ISNATLIST(mark(X)) → ISNATLIST(X)
ISNATLIST(active(X)) → ISNATLIST(X)
U611(mark(X1), X2) → U611(X1, X2)
U611(X1, mark(X2)) → U611(X1, X2)
U611(active(X1), X2) → U611(X1, X2)
U611(X1, active(X2)) → U611(X1, X2)
U621(mark(X)) → U621(X)
U621(active(X)) → U621(X)
U711(mark(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, mark(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, mark(X3)) → U711(X1, X2, X3)
U711(active(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, active(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, active(X3)) → U711(X1, X2, X3)
U721(mark(X1), X2) → U721(X1, X2)
U721(X1, mark(X2)) → U721(X1, X2)
U721(active(X1), X2) → U721(X1, X2)
U721(X1, active(X2)) → U721(X1, X2)
ISNAT(mark(X)) → ISNAT(X)
ISNAT(active(X)) → ISNAT(X)
S(mark(X)) → S(X)
S(active(X)) → S(X)
LENGTH(mark(X)) → LENGTH(X)
LENGTH(active(X)) → LENGTH(X)
U811(mark(X)) → U811(X)
U811(active(X)) → U811(X)
U911(mark(X1), X2, X3, X4) → U911(X1, X2, X3, X4)
U911(X1, mark(X2), X3, X4) → U911(X1, X2, X3, X4)
U911(X1, X2, mark(X3), X4) → U911(X1, X2, X3, X4)
U911(X1, X2, X3, mark(X4)) → U911(X1, X2, X3, X4)
U911(active(X1), X2, X3, X4) → U911(X1, X2, X3, X4)
U911(X1, active(X2), X3, X4) → U911(X1, X2, X3, X4)
U911(X1, X2, active(X3), X4) → U911(X1, X2, X3, X4)
U911(X1, X2, X3, active(X4)) → U911(X1, X2, X3, X4)
U921(mark(X1), X2, X3, X4) → U921(X1, X2, X3, X4)
U921(X1, mark(X2), X3, X4) → U921(X1, X2, X3, X4)
U921(X1, X2, mark(X3), X4) → U921(X1, X2, X3, X4)
U921(X1, X2, X3, mark(X4)) → U921(X1, X2, X3, X4)
U921(active(X1), X2, X3, X4) → U921(X1, X2, X3, X4)
U921(X1, active(X2), X3, X4) → U921(X1, X2, X3, X4)
U921(X1, X2, active(X3), X4) → U921(X1, X2, X3, X4)
U921(X1, X2, X3, active(X4)) → U921(X1, X2, X3, X4)
U931(mark(X1), X2, X3, X4) → U931(X1, X2, X3, X4)
U931(X1, mark(X2), X3, X4) → U931(X1, X2, X3, X4)
U931(X1, X2, mark(X3), X4) → U931(X1, X2, X3, X4)
U931(X1, X2, X3, mark(X4)) → U931(X1, X2, X3, X4)
U931(active(X1), X2, X3, X4) → U931(X1, X2, X3, X4)
U931(X1, active(X2), X3, X4) → U931(X1, X2, X3, X4)
U931(X1, X2, active(X3), X4) → U931(X1, X2, X3, X4)
U931(X1, X2, X3, active(X4)) → U931(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
TAKE(X1, mark(X2)) → TAKE(X1, X2)
TAKE(mark(X1), X2) → TAKE(X1, X2)
TAKE(active(X1), X2) → TAKE(X1, X2)
TAKE(X1, active(X2)) → TAKE(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
TAKE(X1, mark(X2)) → TAKE(X1, X2)
TAKE(mark(X1), X2) → TAKE(X1, X2)
TAKE(active(X1), X2) → TAKE(X1, X2)
TAKE(X1, active(X2)) → TAKE(X1, X2)
TAKE2 > active1
zeros > cons > U51 > U52 > mark1 > active1
zeros > cons > U51 > U52 > tt > active1
zeros > cons > isNat1 > U11 > mark1 > active1
zeros > cons > isNat1 > U11 > tt > active1
zeros > cons > isNat1 > U21 > mark1 > active1
zeros > cons > isNat1 > U21 > tt > active1
zeros > 0 > U81 > nil > mark1 > active1
zeros > 0 > U81 > nil > tt > active1
isNatIList > U31 > mark1 > active1
isNatIList > U31 > tt > active1
isNatIList > U41 > U42 > mark1 > active1
isNatIList > U41 > U42 > tt > active1
isNatIList > isNat1 > U11 > mark1 > active1
isNatIList > isNat1 > U11 > tt > active1
isNatIList > isNat1 > U21 > mark1 > active1
isNatIList > isNat1 > U21 > tt > active1
isNatList > U51 > U52 > mark1 > active1
isNatList > U51 > U52 > tt > active1
isNatList > U61 > U62 > mark1 > active1
isNatList > U61 > U62 > tt > active1
isNatList > isNat1 > U11 > mark1 > active1
isNatList > isNat1 > U11 > tt > active1
isNatList > isNat1 > U21 > mark1 > active1
isNatList > isNat1 > U21 > tt > active1
length > 0 > U81 > nil > mark1 > active1
length > 0 > U81 > nil > tt > active1
length > U71 > U72 > mark1 > active1
length > U71 > U72 > s > active1
length > U71 > isNat1 > U11 > mark1 > active1
length > U71 > isNat1 > U11 > tt > active1
length > U71 > isNat1 > U21 > mark1 > active1
length > U71 > isNat1 > U21 > tt > active1
take > U61 > U62 > mark1 > active1
take > U61 > U62 > tt > active1
take > U81 > nil > mark1 > active1
take > U81 > nil > tt > active1
take > U91 > U92 > U93 > cons > U51 > U52 > mark1 > active1
take > U91 > U92 > U93 > cons > U51 > U52 > tt > active1
take > U91 > U92 > U93 > cons > isNat1 > U11 > mark1 > active1
take > U91 > U92 > U93 > cons > isNat1 > U11 > tt > active1
take > U91 > U92 > U93 > cons > isNat1 > U21 > mark1 > active1
take > U91 > U92 > U93 > cons > isNat1 > U21 > tt > active1
TAKE2: [2,1]
mark1: multiset
active1: multiset
zeros: multiset
cons: []
0: multiset
U11: multiset
tt: multiset
U21: multiset
U31: multiset
U41: multiset
U42: []
isNatIList: []
U51: []
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat1: [1]
s: []
length: []
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U931(X1, mark(X2), X3, X4) → U931(X1, X2, X3, X4)
U931(mark(X1), X2, X3, X4) → U931(X1, X2, X3, X4)
U931(X1, X2, mark(X3), X4) → U931(X1, X2, X3, X4)
U931(X1, X2, X3, mark(X4)) → U931(X1, X2, X3, X4)
U931(active(X1), X2, X3, X4) → U931(X1, X2, X3, X4)
U931(X1, active(X2), X3, X4) → U931(X1, X2, X3, X4)
U931(X1, X2, active(X3), X4) → U931(X1, X2, X3, X4)
U931(X1, X2, X3, active(X4)) → U931(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U931(mark(X1), X2, X3, X4) → U931(X1, X2, X3, X4)
U931(active(X1), X2, X3, X4) → U931(X1, X2, X3, X4)
zeros > 0 > tt > U92 > U93 > mark1 > cons > active1
zeros > 0 > tt > U92 > U93 > mark1 > U911 > active1
length > 0 > tt > U92 > U93 > mark1 > cons > active1
length > 0 > tt > U92 > U93 > mark1 > U911 > active1
length > U11 > tt > U92 > U93 > mark1 > cons > active1
length > U11 > tt > U92 > U93 > mark1 > U911 > active1
length > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > cons > active1
length > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > U911 > active1
length > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > cons > active1
length > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > U911 > active1
length > U71 > U72 > s > U21 > tt > U92 > U93 > mark1 > cons > active1
length > U71 > U72 > s > U21 > tt > U92 > U93 > mark1 > U911 > active1
take > isNatIList > U31 > tt > U92 > U93 > mark1 > cons > active1
take > isNatIList > U31 > tt > U92 > U93 > mark1 > U911 > active1
take > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > cons > active1
take > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > U911 > active1
take > isNatIList > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > cons > active1
take > isNatIList > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > U911 > active1
take > isNatIList > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > cons > active1
take > isNatIList > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > U911 > active1
take > isNat > U11 > tt > U92 > U93 > mark1 > cons > active1
take > isNat > U11 > tt > U92 > U93 > mark1 > U911 > active1
take > isNat > U21 > tt > U92 > U93 > mark1 > cons > active1
take > isNat > U21 > tt > U92 > U93 > mark1 > U911 > active1
take > isNat > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > cons > active1
take > isNat > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > U911 > active1
take > isNat > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > cons > active1
take > isNat > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > U911 > active1
take > U81 > nil > tt > U92 > U93 > mark1 > cons > active1
take > U81 > nil > tt > U92 > U93 > mark1 > U911 > active1
mark1: [1]
active1: multiset
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: []
U42: []
isNatIList: multiset
U51: []
U52: []
isNatList: []
U61: multiset
U62: multiset
U71: []
U72: []
isNat: []
s: multiset
length: []
U81: []
nil: multiset
U911: [1]
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U931(X1, mark(X2), X3, X4) → U931(X1, X2, X3, X4)
U931(X1, X2, mark(X3), X4) → U931(X1, X2, X3, X4)
U931(X1, X2, X3, mark(X4)) → U931(X1, X2, X3, X4)
U931(X1, active(X2), X3, X4) → U931(X1, X2, X3, X4)
U931(X1, X2, active(X3), X4) → U931(X1, X2, X3, X4)
U931(X1, X2, X3, active(X4)) → U931(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U931(X1, mark(X2), X3, X4) → U931(X1, X2, X3, X4)
U931(X1, X2, mark(X3), X4) → U931(X1, X2, X3, X4)
U931(X1, X2, X3, mark(X4)) → U931(X1, X2, X3, X4)
zeros > 0 > U81 > mark1 > cons > isNat1 > U93^14
zeros > 0 > U81 > mark1 > nil > tt > isNat1 > U93^14
isNatIList1 > U31 > mark1 > cons > isNat1 > U93^14
isNatIList1 > U31 > mark1 > nil > tt > isNat1 > U93^14
isNatIList1 > U41 > U42 > mark1 > cons > isNat1 > U93^14
isNatIList1 > U41 > U42 > mark1 > nil > tt > isNat1 > U93^14
isNatList1 > U51 > U52 > mark1 > cons > isNat1 > U93^14
isNatList1 > U51 > U52 > mark1 > nil > tt > isNat1 > U93^14
isNatList1 > U61 > U62 > mark1 > cons > isNat1 > U93^14
isNatList1 > U61 > U62 > mark1 > nil > tt > isNat1 > U93^14
length > 0 > U81 > mark1 > cons > isNat1 > U93^14
length > 0 > U81 > mark1 > nil > tt > isNat1 > U93^14
length > U11 > mark1 > cons > isNat1 > U93^14
length > U11 > mark1 > nil > tt > isNat1 > U93^14
length > U71 > U72 > s > U21 > mark1 > cons > isNat1 > U93^14
length > U71 > U72 > s > U21 > mark1 > nil > tt > isNat1 > U93^14
length > U71 > U72 > s > U91 > U92 > U93 > mark1 > cons > isNat1 > U93^14
length > U71 > U72 > s > U91 > U92 > U93 > mark1 > nil > tt > isNat1 > U93^14
U93^14: [3,1,4,2]
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: []
U42: multiset
isNatIList1: [1]
U51: multiset
U52: []
isNatList1: [1]
U61: multiset
U62: []
U71: []
U72: []
isNat1: multiset
s: []
length: []
U81: []
nil: multiset
U91: []
U92: []
U93: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U931(X1, active(X2), X3, X4) → U931(X1, X2, X3, X4)
U931(X1, X2, active(X3), X4) → U931(X1, X2, X3, X4)
U931(X1, X2, X3, active(X4)) → U931(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U931(X1, X2, X3, active(X4)) → U931(X1, X2, X3, X4)
zeros > cons > U71 > U72 > mark1 > active1 > U93^11 > U811
zeros > cons > U71 > U72 > mark1 > active1 > 0 > U811
zeros > cons > U71 > U72 > mark1 > active1 > s > U811
zeros > cons > U71 > U72 > mark1 > active1 > length1 > U811
zeros > tt > U72 > mark1 > active1 > U93^11 > U811
zeros > tt > U72 > mark1 > active1 > 0 > U811
zeros > tt > U72 > mark1 > active1 > s > U811
zeros > tt > U72 > mark1 > active1 > length1 > U811
zeros > tt > nil > mark1 > active1 > U93^11 > U811
zeros > tt > nil > mark1 > active1 > 0 > U811
zeros > tt > nil > mark1 > active1 > s > U811
zeros > tt > nil > mark1 > active1 > length1 > U811
isNatList > U51 > U52 > tt > U72 > mark1 > active1 > U93^11 > U811
isNatList > U51 > U52 > tt > U72 > mark1 > active1 > 0 > U811
isNatList > U51 > U52 > tt > U72 > mark1 > active1 > s > U811
isNatList > U51 > U52 > tt > U72 > mark1 > active1 > length1 > U811
isNatList > U51 > U52 > tt > nil > mark1 > active1 > U93^11 > U811
isNatList > U51 > U52 > tt > nil > mark1 > active1 > 0 > U811
isNatList > U51 > U52 > tt > nil > mark1 > active1 > s > U811
isNatList > U51 > U52 > tt > nil > mark1 > active1 > length1 > U811
isNatList > U61 > U62 > tt > U72 > mark1 > active1 > U93^11 > U811
isNatList > U61 > U62 > tt > U72 > mark1 > active1 > 0 > U811
isNatList > U61 > U62 > tt > U72 > mark1 > active1 > s > U811
isNatList > U61 > U62 > tt > U72 > mark1 > active1 > length1 > U811
isNatList > U61 > U62 > tt > nil > mark1 > active1 > U93^11 > U811
isNatList > U61 > U62 > tt > nil > mark1 > active1 > 0 > U811
isNatList > U61 > U62 > tt > nil > mark1 > active1 > s > U811
isNatList > U61 > U62 > tt > nil > mark1 > active1 > length1 > U811
isNatList > isNat > U11 > tt > U72 > mark1 > active1 > U93^11 > U811
isNatList > isNat > U11 > tt > U72 > mark1 > active1 > 0 > U811
isNatList > isNat > U11 > tt > U72 > mark1 > active1 > s > U811
isNatList > isNat > U11 > tt > U72 > mark1 > active1 > length1 > U811
isNatList > isNat > U11 > tt > nil > mark1 > active1 > U93^11 > U811
isNatList > isNat > U11 > tt > nil > mark1 > active1 > 0 > U811
isNatList > isNat > U11 > tt > nil > mark1 > active1 > s > U811
isNatList > isNat > U11 > tt > nil > mark1 > active1 > length1 > U811
isNatList > isNat > U21 > tt > U72 > mark1 > active1 > U93^11 > U811
isNatList > isNat > U21 > tt > U72 > mark1 > active1 > 0 > U811
isNatList > isNat > U21 > tt > U72 > mark1 > active1 > s > U811
isNatList > isNat > U21 > tt > U72 > mark1 > active1 > length1 > U811
isNatList > isNat > U21 > tt > nil > mark1 > active1 > U93^11 > U811
isNatList > isNat > U21 > tt > nil > mark1 > active1 > 0 > U811
isNatList > isNat > U21 > tt > nil > mark1 > active1 > s > U811
isNatList > isNat > U21 > tt > nil > mark1 > active1 > length1 > U811
take > isNatIList > U31 > tt > U72 > mark1 > active1 > U93^11 > U811
take > isNatIList > U31 > tt > U72 > mark1 > active1 > 0 > U811
take > isNatIList > U31 > tt > U72 > mark1 > active1 > s > U811
take > isNatIList > U31 > tt > U72 > mark1 > active1 > length1 > U811
take > isNatIList > U31 > tt > nil > mark1 > active1 > U93^11 > U811
take > isNatIList > U31 > tt > nil > mark1 > active1 > 0 > U811
take > isNatIList > U31 > tt > nil > mark1 > active1 > s > U811
take > isNatIList > U31 > tt > nil > mark1 > active1 > length1 > U811
take > isNatIList > U41 > U42 > tt > U72 > mark1 > active1 > U93^11 > U811
take > isNatIList > U41 > U42 > tt > U72 > mark1 > active1 > 0 > U811
take > isNatIList > U41 > U42 > tt > U72 > mark1 > active1 > s > U811
take > isNatIList > U41 > U42 > tt > U72 > mark1 > active1 > length1 > U811
take > isNatIList > U41 > U42 > tt > nil > mark1 > active1 > U93^11 > U811
take > isNatIList > U41 > U42 > tt > nil > mark1 > active1 > 0 > U811
take > isNatIList > U41 > U42 > tt > nil > mark1 > active1 > s > U811
take > isNatIList > U41 > U42 > tt > nil > mark1 > active1 > length1 > U811
take > isNatIList > isNat > U11 > tt > U72 > mark1 > active1 > U93^11 > U811
take > isNatIList > isNat > U11 > tt > U72 > mark1 > active1 > 0 > U811
take > isNatIList > isNat > U11 > tt > U72 > mark1 > active1 > s > U811
take > isNatIList > isNat > U11 > tt > U72 > mark1 > active1 > length1 > U811
take > isNatIList > isNat > U11 > tt > nil > mark1 > active1 > U93^11 > U811
take > isNatIList > isNat > U11 > tt > nil > mark1 > active1 > 0 > U811
take > isNatIList > isNat > U11 > tt > nil > mark1 > active1 > s > U811
take > isNatIList > isNat > U11 > tt > nil > mark1 > active1 > length1 > U811
take > isNatIList > isNat > U21 > tt > U72 > mark1 > active1 > U93^11 > U811
take > isNatIList > isNat > U21 > tt > U72 > mark1 > active1 > 0 > U811
take > isNatIList > isNat > U21 > tt > U72 > mark1 > active1 > s > U811
take > isNatIList > isNat > U21 > tt > U72 > mark1 > active1 > length1 > U811
take > isNatIList > isNat > U21 > tt > nil > mark1 > active1 > U93^11 > U811
take > isNatIList > isNat > U21 > tt > nil > mark1 > active1 > 0 > U811
take > isNatIList > isNat > U21 > tt > nil > mark1 > active1 > s > U811
take > isNatIList > isNat > U21 > tt > nil > mark1 > active1 > length1 > U811
take > U61 > U62 > tt > U72 > mark1 > active1 > U93^11 > U811
take > U61 > U62 > tt > U72 > mark1 > active1 > 0 > U811
take > U61 > U62 > tt > U72 > mark1 > active1 > s > U811
take > U61 > U62 > tt > U72 > mark1 > active1 > length1 > U811
take > U61 > U62 > tt > nil > mark1 > active1 > U93^11 > U811
take > U61 > U62 > tt > nil > mark1 > active1 > 0 > U811
take > U61 > U62 > tt > nil > mark1 > active1 > s > U811
take > U61 > U62 > tt > nil > mark1 > active1 > length1 > U811
take > U91 > U92 > isNat > U11 > tt > U72 > mark1 > active1 > U93^11 > U811
take > U91 > U92 > isNat > U11 > tt > U72 > mark1 > active1 > 0 > U811
take > U91 > U92 > isNat > U11 > tt > U72 > mark1 > active1 > s > U811
take > U91 > U92 > isNat > U11 > tt > U72 > mark1 > active1 > length1 > U811
take > U91 > U92 > isNat > U11 > tt > nil > mark1 > active1 > U93^11 > U811
take > U91 > U92 > isNat > U11 > tt > nil > mark1 > active1 > 0 > U811
take > U91 > U92 > isNat > U11 > tt > nil > mark1 > active1 > s > U811
take > U91 > U92 > isNat > U11 > tt > nil > mark1 > active1 > length1 > U811
take > U91 > U92 > isNat > U21 > tt > U72 > mark1 > active1 > U93^11 > U811
take > U91 > U92 > isNat > U21 > tt > U72 > mark1 > active1 > 0 > U811
take > U91 > U92 > isNat > U21 > tt > U72 > mark1 > active1 > s > U811
take > U91 > U92 > isNat > U21 > tt > U72 > mark1 > active1 > length1 > U811
take > U91 > U92 > isNat > U21 > tt > nil > mark1 > active1 > U93^11 > U811
take > U91 > U92 > isNat > U21 > tt > nil > mark1 > active1 > 0 > U811
take > U91 > U92 > isNat > U21 > tt > nil > mark1 > active1 > s > U811
take > U91 > U92 > isNat > U21 > tt > nil > mark1 > active1 > length1 > U811
take > U91 > U92 > U93 > cons > U71 > U72 > mark1 > active1 > U93^11 > U811
take > U91 > U92 > U93 > cons > U71 > U72 > mark1 > active1 > 0 > U811
take > U91 > U92 > U93 > cons > U71 > U72 > mark1 > active1 > s > U811
take > U91 > U92 > U93 > cons > U71 > U72 > mark1 > active1 > length1 > U811
U93^11: multiset
active1: multiset
zeros: multiset
mark1: [1]
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: []
U42: []
isNatIList: multiset
U51: []
U52: []
isNatList: []
U61: []
U62: []
U71: multiset
U72: []
isNat: []
s: []
length1: multiset
U811: multiset
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U931(X1, active(X2), X3, X4) → U931(X1, X2, X3, X4)
U931(X1, X2, active(X3), X4) → U931(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U931(X1, active(X2), X3, X4) → U931(X1, X2, X3, X4)
zeros > tt > U72 > s > mark1 > active1 > cons > U93^11
zeros > tt > nil > 0 > mark1 > active1 > cons > U93^11
zeros > tt > U93 > mark1 > active1 > cons > U93^11
isNatIList1 > U31 > tt > U72 > s > mark1 > active1 > cons > U93^11
isNatIList1 > U31 > tt > nil > 0 > mark1 > active1 > cons > U93^11
isNatIList1 > U31 > tt > U93 > mark1 > active1 > cons > U93^11
isNatIList1 > U41 > U42 > tt > U72 > s > mark1 > active1 > cons > U93^11
isNatIList1 > U41 > U42 > tt > nil > 0 > mark1 > active1 > cons > U93^11
isNatIList1 > U41 > U42 > tt > U93 > mark1 > active1 > cons > U93^11
isNatIList1 > isNat1 > U21 > tt > U72 > s > mark1 > active1 > cons > U93^11
isNatIList1 > isNat1 > U21 > tt > nil > 0 > mark1 > active1 > cons > U93^11
isNatIList1 > isNat1 > U21 > tt > U93 > mark1 > active1 > cons > U93^11
isNatList > U51 > U52 > tt > U72 > s > mark1 > active1 > cons > U93^11
isNatList > U51 > U52 > tt > nil > 0 > mark1 > active1 > cons > U93^11
isNatList > U51 > U52 > tt > U93 > mark1 > active1 > cons > U93^11
isNatList > U61 > U62 > tt > U72 > s > mark1 > active1 > cons > U93^11
isNatList > U61 > U62 > tt > nil > 0 > mark1 > active1 > cons > U93^11
isNatList > U61 > U62 > tt > U93 > mark1 > active1 > cons > U93^11
isNatList > isNat1 > U21 > tt > U72 > s > mark1 > active1 > cons > U93^11
isNatList > isNat1 > U21 > tt > nil > 0 > mark1 > active1 > cons > U93^11
isNatList > isNat1 > U21 > tt > U93 > mark1 > active1 > cons > U93^11
length > U11 > tt > U72 > s > mark1 > active1 > cons > U93^11
length > U11 > tt > nil > 0 > mark1 > active1 > cons > U93^11
length > U11 > tt > U93 > mark1 > active1 > cons > U93^11
length > U71 > U72 > s > mark1 > active1 > cons > U93^11
take > U61 > U62 > tt > U72 > s > mark1 > active1 > cons > U93^11
take > U61 > U62 > tt > nil > 0 > mark1 > active1 > cons > U93^11
take > U61 > U62 > tt > U93 > mark1 > active1 > cons > U93^11
take > isNat1 > U21 > tt > U72 > s > mark1 > active1 > cons > U93^11
take > isNat1 > U21 > tt > nil > 0 > mark1 > active1 > cons > U93^11
take > isNat1 > U21 > tt > U93 > mark1 > active1 > cons > U93^11
take > U81 > nil > 0 > mark1 > active1 > cons > U93^11
take > U91 > U92 > U93 > mark1 > active1 > cons > U93^11
U93^11: [1]
active1: multiset
zeros: multiset
mark1: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: []
U42: []
isNatIList1: [1]
U51: []
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: multiset
isNat1: [1]
s: multiset
length: []
U81: []
nil: multiset
U91: multiset
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U931(X1, X2, active(X3), X4) → U931(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U931(X1, X2, active(X3), X4) → U931(X1, X2, X3, X4)
zeros > cons > U41 > U42 > tt > U72 > mark1 > active1 > 0 > U711
zeros > cons > U41 > U42 > tt > U72 > mark1 > s > U711
zeros > cons > U41 > U42 > tt > U72 > mark1 > length1 > 0 > U711
zeros > cons > isNatIList1 > U31 > tt > U72 > mark1 > active1 > 0 > U711
zeros > cons > isNatIList1 > U31 > tt > U72 > mark1 > s > U711
zeros > cons > isNatIList1 > U31 > tt > U72 > mark1 > length1 > 0 > U711
zeros > cons > isNatList > U51 > U52 > tt > U72 > mark1 > active1 > 0 > U711
zeros > cons > isNatList > U51 > U52 > tt > U72 > mark1 > s > U711
zeros > cons > isNatList > U51 > U52 > tt > U72 > mark1 > length1 > 0 > U711
zeros > cons > isNatList > U61 > U62 > tt > U72 > mark1 > active1 > 0 > U711
zeros > cons > isNatList > U61 > U62 > tt > U72 > mark1 > s > U711
zeros > cons > isNatList > U61 > U62 > tt > U72 > mark1 > length1 > 0 > U711
zeros > cons > isNat > U11 > tt > U72 > mark1 > active1 > 0 > U711
zeros > cons > isNat > U11 > tt > U72 > mark1 > s > U711
zeros > cons > isNat > U11 > tt > U72 > mark1 > length1 > 0 > U711
zeros > cons > isNat > U21 > tt > U72 > mark1 > active1 > 0 > U711
zeros > cons > isNat > U21 > tt > U72 > mark1 > s > U711
zeros > cons > isNat > U21 > tt > U72 > mark1 > length1 > 0 > U711
take > U81 > nil > tt > U72 > mark1 > active1 > 0 > U711
take > U81 > nil > tt > U72 > mark1 > s > U711
take > U81 > nil > tt > U72 > mark1 > length1 > 0 > U711
take > U91 > U92 > U93 > cons > U41 > U42 > tt > U72 > mark1 > active1 > 0 > U711
take > U91 > U92 > U93 > cons > U41 > U42 > tt > U72 > mark1 > s > U711
take > U91 > U92 > U93 > cons > U41 > U42 > tt > U72 > mark1 > length1 > 0 > U711
take > U91 > U92 > U93 > cons > isNatIList1 > U31 > tt > U72 > mark1 > active1 > 0 > U711
take > U91 > U92 > U93 > cons > isNatIList1 > U31 > tt > U72 > mark1 > s > U711
take > U91 > U92 > U93 > cons > isNatIList1 > U31 > tt > U72 > mark1 > length1 > 0 > U711
take > U91 > U92 > U93 > cons > isNatList > U51 > U52 > tt > U72 > mark1 > active1 > 0 > U711
take > U91 > U92 > U93 > cons > isNatList > U51 > U52 > tt > U72 > mark1 > s > U711
take > U91 > U92 > U93 > cons > isNatList > U51 > U52 > tt > U72 > mark1 > length1 > 0 > U711
take > U91 > U92 > U93 > cons > isNatList > U61 > U62 > tt > U72 > mark1 > active1 > 0 > U711
take > U91 > U92 > U93 > cons > isNatList > U61 > U62 > tt > U72 > mark1 > s > U711
take > U91 > U92 > U93 > cons > isNatList > U61 > U62 > tt > U72 > mark1 > length1 > 0 > U711
take > U91 > U92 > U93 > cons > isNat > U11 > tt > U72 > mark1 > active1 > 0 > U711
take > U91 > U92 > U93 > cons > isNat > U11 > tt > U72 > mark1 > s > U711
take > U91 > U92 > U93 > cons > isNat > U11 > tt > U72 > mark1 > length1 > 0 > U711
take > U91 > U92 > U93 > cons > isNat > U21 > tt > U72 > mark1 > active1 > 0 > U711
take > U91 > U92 > U93 > cons > isNat > U21 > tt > U72 > mark1 > s > U711
take > U91 > U92 > U93 > cons > isNat > U21 > tt > U72 > mark1 > length1 > 0 > U711
active1: multiset
zeros: multiset
mark1: [1]
cons: []
0: multiset
U11: multiset
tt: multiset
U21: multiset
U31: []
U41: []
U42: multiset
isNatIList1: [1]
U51: []
U52: multiset
isNatList: []
U61: []
U62: []
U711: multiset
U72: []
isNat: []
s: multiset
length1: [1]
U81: multiset
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U921(X1, mark(X2), X3, X4) → U921(X1, X2, X3, X4)
U921(mark(X1), X2, X3, X4) → U921(X1, X2, X3, X4)
U921(X1, X2, mark(X3), X4) → U921(X1, X2, X3, X4)
U921(X1, X2, X3, mark(X4)) → U921(X1, X2, X3, X4)
U921(active(X1), X2, X3, X4) → U921(X1, X2, X3, X4)
U921(X1, active(X2), X3, X4) → U921(X1, X2, X3, X4)
U921(X1, X2, active(X3), X4) → U921(X1, X2, X3, X4)
U921(X1, X2, X3, active(X4)) → U921(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U921(mark(X1), X2, X3, X4) → U921(X1, X2, X3, X4)
U921(X1, X2, mark(X3), X4) → U921(X1, X2, X3, X4)
U921(X1, X2, X3, mark(X4)) → U921(X1, X2, X3, X4)
U921(active(X1), X2, X3, X4) → U921(X1, X2, X3, X4)
U921(X1, X2, active(X3), X4) → U921(X1, X2, X3, X4)
U921(X1, X2, X3, active(X4)) → U921(X1, X2, X3, X4)
zeros > tt > nil > active1 > U92^13
zeros > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
zeros > tt > U92 > U93 > cons > U911 > active1 > U92^13
isNatList > U51 > U52 > tt > nil > active1 > U92^13
isNatList > U51 > U52 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
isNatList > U51 > U52 > tt > U92 > U93 > cons > U911 > active1 > U92^13
isNatList > U61 > isNatIList > U31 > tt > nil > active1 > U92^13
isNatList > U61 > isNatIList > U31 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
isNatList > U61 > isNatIList > U31 > tt > U92 > U93 > cons > U911 > active1 > U92^13
isNatList > U61 > isNatIList > U41 > U42 > tt > nil > active1 > U92^13
isNatList > U61 > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
isNatList > U61 > isNatIList > U41 > U42 > tt > U92 > U93 > cons > U911 > active1 > U92^13
isNatList > U61 > U62 > tt > nil > active1 > U92^13
isNatList > U61 > U62 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
isNatList > U61 > U62 > tt > U92 > U93 > cons > U911 > active1 > U92^13
isNatList > isNat > U11 > tt > nil > active1 > U92^13
isNatList > isNat > U11 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
isNatList > isNat > U11 > tt > U92 > U93 > cons > U911 > active1 > U92^13
isNatList > isNat > U21 > tt > nil > active1 > U92^13
isNatList > isNat > U21 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
isNatList > isNat > U21 > tt > U92 > U93 > cons > U911 > active1 > U92^13
length > 0 > isNatIList > U31 > tt > nil > active1 > U92^13
length > 0 > isNatIList > U31 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
length > 0 > isNatIList > U31 > tt > U92 > U93 > cons > U911 > active1 > U92^13
length > 0 > isNatIList > U41 > U42 > tt > nil > active1 > U92^13
length > 0 > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
length > 0 > isNatIList > U41 > U42 > tt > U92 > U93 > cons > U911 > active1 > U92^13
length > 0 > U81 > mark1 > take1 > U911 > active1 > U92^13
length > 0 > U81 > nil > active1 > U92^13
length > U71 > U72 > s > U21 > tt > nil > active1 > U92^13
length > U71 > U72 > s > U21 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
length > U71 > U72 > s > U21 > tt > U92 > U93 > cons > U911 > active1 > U92^13
length > U71 > U72 > s > isNatIList > U31 > tt > nil > active1 > U92^13
length > U71 > U72 > s > isNatIList > U31 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
length > U71 > U72 > s > isNatIList > U31 > tt > U92 > U93 > cons > U911 > active1 > U92^13
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > nil > active1 > U92^13
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > U92 > U93 > cons > U911 > active1 > U92^13
length > U71 > isNat > U11 > tt > nil > active1 > U92^13
length > U71 > isNat > U11 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
length > U71 > isNat > U11 > tt > U92 > U93 > cons > U911 > active1 > U92^13
length > U71 > isNat > U21 > tt > nil > active1 > U92^13
length > U71 > isNat > U21 > tt > U92 > U93 > mark1 > take1 > U911 > active1 > U92^13
length > U71 > isNat > U21 > tt > U92 > U93 > cons > U911 > active1 > U92^13
U92^13: [3,1,2]
mark1: [1]
active1: multiset
zeros: multiset
cons: []
0: multiset
U11: []
tt: multiset
U21: []
U31: multiset
U41: []
U42: multiset
isNatIList: []
U51: []
U52: []
isNatList: []
U61: []
U62: []
U71: multiset
U72: []
isNat: []
s: []
length: []
U81: []
nil: multiset
U911: [1]
U92: []
U93: []
take1: [1]
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U921(X1, mark(X2), X3, X4) → U921(X1, X2, X3, X4)
U921(X1, active(X2), X3, X4) → U921(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U921(X1, mark(X2), X3, X4) → U921(X1, X2, X3, X4)
U921(X1, active(X2), X3, X4) → U921(X1, X2, X3, X4)
zeros > mark1 > tt > active1 > cons
zeros > mark1 > take2 > active1 > cons
isNatIList1 > U31 > mark1 > tt > active1 > cons
isNatIList1 > U31 > mark1 > take2 > active1 > cons
isNatIList1 > U41 > U42 > mark1 > tt > active1 > cons
isNatIList1 > U41 > U42 > mark1 > take2 > active1 > cons
isNatIList1 > isNat > U11 > mark1 > tt > active1 > cons
isNatIList1 > isNat > U11 > mark1 > take2 > active1 > cons
isNatIList1 > isNat > U21 > mark1 > tt > active1 > cons
isNatIList1 > isNat > U21 > mark1 > take2 > active1 > cons
isNatIList1 > isNat > isNatList1 > U51 > U52 > mark1 > tt > active1 > cons
isNatIList1 > isNat > isNatList1 > U51 > U52 > mark1 > take2 > active1 > cons
isNatIList1 > isNat > isNatList1 > U611 > U62 > mark1 > tt > active1 > cons
isNatIList1 > isNat > isNatList1 > U611 > U62 > mark1 > take2 > active1 > cons
length > 0 > U81 > mark1 > tt > active1 > cons
length > 0 > U81 > mark1 > take2 > active1 > cons
length > 0 > U81 > nil > tt > active1 > cons
length > U71 > U72 > s > U91 > U92 > U93 > mark1 > tt > active1 > cons
length > U71 > U72 > s > U91 > U92 > U93 > mark1 > take2 > active1 > cons
length > U71 > isNat > U11 > mark1 > tt > active1 > cons
length > U71 > isNat > U11 > mark1 > take2 > active1 > cons
length > U71 > isNat > U21 > mark1 > tt > active1 > cons
length > U71 > isNat > U21 > mark1 > take2 > active1 > cons
length > U71 > isNat > isNatList1 > U51 > U52 > mark1 > tt > active1 > cons
length > U71 > isNat > isNatList1 > U51 > U52 > mark1 > take2 > active1 > cons
length > U71 > isNat > isNatList1 > U611 > U62 > mark1 > tt > active1 > cons
length > U71 > isNat > isNatList1 > U611 > U62 > mark1 > take2 > active1 > cons
mark1: [1]
active1: multiset
zeros: multiset
cons: []
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: []
isNatIList1: [1]
U51: []
U52: []
isNatList1: [1]
U611: [1]
U62: []
U71: []
U72: []
isNat: []
s: []
length: []
U81: []
nil: multiset
U91: []
U92: []
U93: []
take2: [1,2]
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U911(X1, mark(X2), X3, X4) → U911(X1, X2, X3, X4)
U911(mark(X1), X2, X3, X4) → U911(X1, X2, X3, X4)
U911(X1, X2, mark(X3), X4) → U911(X1, X2, X3, X4)
U911(X1, X2, X3, mark(X4)) → U911(X1, X2, X3, X4)
U911(active(X1), X2, X3, X4) → U911(X1, X2, X3, X4)
U911(X1, active(X2), X3, X4) → U911(X1, X2, X3, X4)
U911(X1, X2, active(X3), X4) → U911(X1, X2, X3, X4)
U911(X1, X2, X3, active(X4)) → U911(X1, X2, X3, X4)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U911(X1, mark(X2), X3, X4) → U911(X1, X2, X3, X4)
U911(mark(X1), X2, X3, X4) → U911(X1, X2, X3, X4)
U911(X1, X2, mark(X3), X4) → U911(X1, X2, X3, X4)
U911(X1, X2, X3, mark(X4)) → U911(X1, X2, X3, X4)
U911(active(X1), X2, X3, X4) → U911(X1, X2, X3, X4)
U911(X1, active(X2), X3, X4) → U911(X1, X2, X3, X4)
U911(X1, X2, active(X3), X4) → U911(X1, X2, X3, X4)
U911(X1, X2, X3, active(X4)) → U911(X1, X2, X3, X4)
zeros > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
zeros > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
isNatIList1 > U31 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
isNatIList1 > U31 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
isNatIList1 > U41 > U42 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
isNatIList1 > U41 > U42 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
isNatIList1 > isNat > U11 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
isNatIList1 > isNat > U11 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
isNatIList1 > isNat > U21 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
isNatIList1 > isNat > U21 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
isNatList > U51 > U52 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
isNatList > U51 > U52 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
isNatList > U61 > U62 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
isNatList > U61 > U62 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
isNatList > isNat > U11 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
isNatList > isNat > U11 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
isNatList > isNat > U21 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
isNatList > isNat > U21 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
length > U71 > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
length > U71 > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
take > U61 > U62 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
take > U61 > U62 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
take > isNat > U11 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
take > isNat > U11 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
take > isNat > U21 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > active1 > nil > U91^14
take > isNat > U21 > tt > U72 > s > U91 > U92 > U93 > cons > mark1 > 0 > U91^14
take > U81 > mark1 > active1 > nil > U91^14
take > U81 > mark1 > 0 > U91^14
U91^14: [3,1,2,4]
mark1: multiset
active1: multiset
zeros: multiset
cons: []
0: multiset
U11: multiset
tt: multiset
U21: []
U31: []
U41: []
U42: []
isNatIList1: multiset
U51: []
U52: []
isNatList: []
U61: multiset
U62: []
U71: []
U72: []
isNat: []
s: []
length: []
U81: multiset
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U811(active(X)) → U811(X)
U811(mark(X)) → U811(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U811(active(X)) → U811(X)
U811(mark(X)) → U811(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
LENGTH(active(X)) → LENGTH(X)
LENGTH(mark(X)) → LENGTH(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
LENGTH(active(X)) → LENGTH(X)
LENGTH(mark(X)) → LENGTH(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
S(active(X)) → S(X)
S(mark(X)) → S(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
S(active(X)) → S(X)
S(mark(X)) → S(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
ISNAT(active(X)) → ISNAT(X)
ISNAT(mark(X)) → ISNAT(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ISNAT(active(X)) → ISNAT(X)
ISNAT(mark(X)) → ISNAT(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U721(X1, mark(X2)) → U721(X1, X2)
U721(mark(X1), X2) → U721(X1, X2)
U721(active(X1), X2) → U721(X1, X2)
U721(X1, active(X2)) → U721(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U721(X1, mark(X2)) → U721(X1, X2)
U721(X1, active(X2)) → U721(X1, X2)
zeros > tt > length > 0 > mark1 > active1 > cons > U72^11
zeros > tt > length > 0 > mark1 > nil > U72^11
zeros > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
zeros > tt > length > U71 > U72 > mark1 > nil > U72^11
zeros > tt > length > U71 > U72 > s > active1 > cons > U72^11
zeros > tt > U92 > U93 > mark1 > active1 > cons > U72^11
zeros > tt > U92 > U93 > mark1 > nil > U72^11
isNatIList > U31 > tt > length > 0 > mark1 > active1 > cons > U72^11
isNatIList > U31 > tt > length > 0 > mark1 > nil > U72^11
isNatIList > U31 > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
isNatIList > U31 > tt > length > U71 > U72 > mark1 > nil > U72^11
isNatIList > U31 > tt > length > U71 > U72 > s > active1 > cons > U72^11
isNatIList > U31 > tt > U92 > U93 > mark1 > active1 > cons > U72^11
isNatIList > U31 > tt > U92 > U93 > mark1 > nil > U72^11
isNatIList > U41 > U42 > tt > length > 0 > mark1 > active1 > cons > U72^11
isNatIList > U41 > U42 > tt > length > 0 > mark1 > nil > U72^11
isNatIList > U41 > U42 > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
isNatIList > U41 > U42 > tt > length > U71 > U72 > mark1 > nil > U72^11
isNatIList > U41 > U42 > tt > length > U71 > U72 > s > active1 > cons > U72^11
isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > active1 > cons > U72^11
isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > nil > U72^11
isNatIList > isNatList > U51 > U52 > tt > length > 0 > mark1 > active1 > cons > U72^11
isNatIList > isNatList > U51 > U52 > tt > length > 0 > mark1 > nil > U72^11
isNatIList > isNatList > U51 > U52 > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
isNatIList > isNatList > U51 > U52 > tt > length > U71 > U72 > mark1 > nil > U72^11
isNatIList > isNatList > U51 > U52 > tt > length > U71 > U72 > s > active1 > cons > U72^11
isNatIList > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > active1 > cons > U72^11
isNatIList > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > nil > U72^11
isNatIList > isNatList > U61 > U62 > tt > length > 0 > mark1 > active1 > cons > U72^11
isNatIList > isNatList > U61 > U62 > tt > length > 0 > mark1 > nil > U72^11
isNatIList > isNatList > U61 > U62 > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
isNatIList > isNatList > U61 > U62 > tt > length > U71 > U72 > mark1 > nil > U72^11
isNatIList > isNatList > U61 > U62 > tt > length > U71 > U72 > s > active1 > cons > U72^11
isNatIList > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > active1 > cons > U72^11
isNatIList > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > nil > U72^11
isNat1 > U11 > tt > length > 0 > mark1 > active1 > cons > U72^11
isNat1 > U11 > tt > length > 0 > mark1 > nil > U72^11
isNat1 > U11 > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
isNat1 > U11 > tt > length > U71 > U72 > mark1 > nil > U72^11
isNat1 > U11 > tt > length > U71 > U72 > s > active1 > cons > U72^11
isNat1 > U11 > tt > U92 > U93 > mark1 > active1 > cons > U72^11
isNat1 > U11 > tt > U92 > U93 > mark1 > nil > U72^11
isNat1 > U21 > tt > length > 0 > mark1 > active1 > cons > U72^11
isNat1 > U21 > tt > length > 0 > mark1 > nil > U72^11
isNat1 > U21 > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
isNat1 > U21 > tt > length > U71 > U72 > mark1 > nil > U72^11
isNat1 > U21 > tt > length > U71 > U72 > s > active1 > cons > U72^11
isNat1 > U21 > tt > U92 > U93 > mark1 > active1 > cons > U72^11
isNat1 > U21 > tt > U92 > U93 > mark1 > nil > U72^11
isNat1 > isNatList > U51 > U52 > tt > length > 0 > mark1 > active1 > cons > U72^11
isNat1 > isNatList > U51 > U52 > tt > length > 0 > mark1 > nil > U72^11
isNat1 > isNatList > U51 > U52 > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
isNat1 > isNatList > U51 > U52 > tt > length > U71 > U72 > mark1 > nil > U72^11
isNat1 > isNatList > U51 > U52 > tt > length > U71 > U72 > s > active1 > cons > U72^11
isNat1 > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > active1 > cons > U72^11
isNat1 > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > nil > U72^11
isNat1 > isNatList > U61 > U62 > tt > length > 0 > mark1 > active1 > cons > U72^11
isNat1 > isNatList > U61 > U62 > tt > length > 0 > mark1 > nil > U72^11
isNat1 > isNatList > U61 > U62 > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
isNat1 > isNatList > U61 > U62 > tt > length > U71 > U72 > mark1 > nil > U72^11
isNat1 > isNatList > U61 > U62 > tt > length > U71 > U72 > s > active1 > cons > U72^11
isNat1 > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > active1 > cons > U72^11
isNat1 > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > nil > U72^11
take > U61 > U62 > tt > length > 0 > mark1 > active1 > cons > U72^11
take > U61 > U62 > tt > length > 0 > mark1 > nil > U72^11
take > U61 > U62 > tt > length > U71 > U72 > mark1 > active1 > cons > U72^11
take > U61 > U62 > tt > length > U71 > U72 > mark1 > nil > U72^11
take > U61 > U62 > tt > length > U71 > U72 > s > active1 > cons > U72^11
take > U61 > U62 > tt > U92 > U93 > mark1 > active1 > cons > U72^11
take > U61 > U62 > tt > U92 > U93 > mark1 > nil > U72^11
take > U81 > mark1 > active1 > cons > U72^11
take > U81 > mark1 > nil > U72^11
take > U91 > U92 > U93 > mark1 > active1 > cons > U72^11
take > U91 > U92 > U93 > mark1 > nil > U72^11
U72^11: multiset
mark1: [1]
active1: multiset
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: []
U31: multiset
U41: []
U42: []
isNatIList: []
U51: []
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat1: [1]
s: []
length: []
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: multiset
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U721(mark(X1), X2) → U721(X1, X2)
U721(active(X1), X2) → U721(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U721(mark(X1), X2) → U721(X1, X2)
U72^11 > cons
zeros > 0 > mark1 > nil > cons
zeros > tt > U72 > s > mark1 > nil > cons
zeros > tt > U92 > U93 > mark1 > nil > cons
isNatIList > U31 > tt > U72 > s > mark1 > nil > cons
isNatIList > U31 > tt > U92 > U93 > mark1 > nil > cons
isNatIList > U41 > U42 > tt > U72 > s > mark1 > nil > cons
isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > nil > cons
isNatIList > isNatList > U51 > U52 > tt > U72 > s > mark1 > nil > cons
isNatIList > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > nil > cons
isNatIList > isNatList > U61 > U62 > tt > U72 > s > mark1 > nil > cons
isNatIList > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > nil > cons
isNat1 > U11 > tt > U72 > s > mark1 > nil > cons
isNat1 > U11 > tt > U92 > U93 > mark1 > nil > cons
isNat1 > U21 > tt > U72 > s > mark1 > nil > cons
isNat1 > U21 > tt > U92 > U93 > mark1 > nil > cons
isNat1 > isNatList > U51 > U52 > tt > U72 > s > mark1 > nil > cons
isNat1 > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > nil > cons
isNat1 > isNatList > U61 > U62 > tt > U72 > s > mark1 > nil > cons
isNat1 > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > nil > cons
length > 0 > mark1 > nil > cons
length > U11 > tt > U72 > s > mark1 > nil > cons
length > U11 > tt > U92 > U93 > mark1 > nil > cons
length > isNatList > U51 > U52 > tt > U72 > s > mark1 > nil > cons
length > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > nil > cons
length > isNatList > U61 > U62 > tt > U72 > s > mark1 > nil > cons
length > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > nil > cons
take > U61 > U62 > tt > U72 > s > mark1 > nil > cons
take > U61 > U62 > tt > U92 > U93 > mark1 > nil > cons
take > U81 > mark1 > nil > cons
take > U91 > U92 > U93 > mark1 > nil > cons
U72^11: multiset
mark1: [1]
zeros: multiset
cons: []
0: multiset
U11: []
tt: multiset
U21: []
U31: []
U41: []
U42: []
isNatIList: multiset
U51: []
U52: multiset
isNatList: []
U61: multiset
U62: multiset
U72: []
isNat1: [1]
s: multiset
length: []
U81: multiset
nil: multiset
U91: []
U92: []
U93: multiset
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U721(active(X1), X2) → U721(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U721(active(X1), X2) → U721(X1, X2)
U72^12 > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U41 > U42 > tt > length1 > active1
zeros > cons > U41 > isNatIList1 > U31 > mark1 > length1 > active1
zeros > cons > U41 > isNatIList1 > U31 > tt > length1 > active1
zeros > cons > isNatList > U51 > U52 > mark1 > length1 > active1
zeros > cons > isNatList > U51 > U52 > tt > length1 > active1
zeros > cons > isNatList > U61 > U62 > mark1 > length1 > active1
zeros > cons > isNatList > U61 > U62 > tt > length1 > active1
zeros > cons > isNatList > isNat > U11 > mark1 > length1 > active1
zeros > cons > isNatList > isNat > U11 > tt > length1 > active1
zeros > cons > isNatList > isNat > U21 > mark1 > length1 > active1
zeros > cons > isNatList > isNat > U21 > tt > length1 > active1
zeros > cons > U71 > U72 > s > isNatIList1 > U31 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > isNatIList1 > U31 > tt > length1 > active1
zeros > cons > U71 > U72 > s > isNat > U11 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > isNat > U11 > tt > length1 > active1
zeros > cons > U71 > U72 > s > isNat > U21 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > isNat > U21 > tt > length1 > active1
zeros > 0 > isNatIList1 > U31 > mark1 > length1 > active1
zeros > 0 > isNatIList1 > U31 > tt > length1 > active1
take > U81 > nil > 0 > isNatIList1 > U31 > mark1 > length1 > active1
take > U81 > nil > 0 > isNatIList1 > U31 > tt > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > tt > length1 > active1
take > U91 > U92 > U93 > cons > U41 > isNatIList1 > U31 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > isNatIList1 > U31 > tt > length1 > active1
take > U91 > U92 > U93 > cons > isNatList > U51 > U52 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > isNatList > U51 > U52 > tt > length1 > active1
take > U91 > U92 > U93 > cons > isNatList > U61 > U62 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > isNatList > U61 > U62 > tt > length1 > active1
take > U91 > U92 > U93 > cons > isNatList > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > isNatList > isNat > U11 > tt > length1 > active1
take > U91 > U92 > U93 > cons > isNatList > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > isNatList > isNat > U21 > tt > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > isNatIList1 > U31 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > isNatIList1 > U31 > tt > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > isNat > U11 > tt > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > isNat > U21 > tt > length1 > active1
U72^12: multiset
active1: multiset
zeros: multiset
mark1: [1]
cons: []
0: multiset
U11: multiset
tt: multiset
U21: []
U31: []
U41: multiset
U42: multiset
isNatIList1: [1]
U51: []
U52: multiset
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: multiset
s: []
length1: [1]
U81: []
nil: multiset
U91: []
U92: multiset
U93: multiset
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U711(X1, mark(X2), X3) → U711(X1, X2, X3)
U711(mark(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, X2, mark(X3)) → U711(X1, X2, X3)
U711(active(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, active(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, active(X3)) → U711(X1, X2, X3)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U711(mark(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, X2, mark(X3)) → U711(X1, X2, X3)
zeros > 0 > isNatIList > U31 > tt > nil > mark1 > U811 > U71^12
zeros > 0 > isNatIList > U31 > tt > nil > mark1 > U911 > U71^12
zeros > 0 > isNatIList > U31 > tt > U92 > U93 > mark1 > U811 > U71^12
zeros > 0 > isNatIList > U31 > tt > U92 > U93 > mark1 > U911 > U71^12
zeros > 0 > isNatIList > U31 > tt > U92 > U93 > cons > U911 > U71^12
zeros > 0 > isNatIList > U41 > U42 > tt > nil > mark1 > U811 > U71^12
zeros > 0 > isNatIList > U41 > U42 > tt > nil > mark1 > U911 > U71^12
zeros > 0 > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > U811 > U71^12
zeros > 0 > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > U911 > U71^12
zeros > 0 > isNatIList > U41 > U42 > tt > U92 > U93 > cons > U911 > U71^12
length > 0 > isNatIList > U31 > tt > nil > mark1 > U811 > U71^12
length > 0 > isNatIList > U31 > tt > nil > mark1 > U911 > U71^12
length > 0 > isNatIList > U31 > tt > U92 > U93 > mark1 > U811 > U71^12
length > 0 > isNatIList > U31 > tt > U92 > U93 > mark1 > U911 > U71^12
length > 0 > isNatIList > U31 > tt > U92 > U93 > cons > U911 > U71^12
length > 0 > isNatIList > U41 > U42 > tt > nil > mark1 > U811 > U71^12
length > 0 > isNatIList > U41 > U42 > tt > nil > mark1 > U911 > U71^12
length > 0 > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > U811 > U71^12
length > 0 > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > U911 > U71^12
length > 0 > isNatIList > U41 > U42 > tt > U92 > U93 > cons > U911 > U71^12
length > U11 > tt > nil > mark1 > U811 > U71^12
length > U11 > tt > nil > mark1 > U911 > U71^12
length > U11 > tt > U92 > U93 > mark1 > U811 > U71^12
length > U11 > tt > U92 > U93 > mark1 > U911 > U71^12
length > U11 > tt > U92 > U93 > cons > U911 > U71^12
length > isNatList > U51 > U52 > tt > nil > mark1 > U811 > U71^12
length > isNatList > U51 > U52 > tt > nil > mark1 > U911 > U71^12
length > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > U811 > U71^12
length > isNatList > U51 > U52 > tt > U92 > U93 > mark1 > U911 > U71^12
length > isNatList > U51 > U52 > tt > U92 > U93 > cons > U911 > U71^12
length > isNatList > U61 > U62 > tt > nil > mark1 > U811 > U71^12
length > isNatList > U61 > U62 > tt > nil > mark1 > U911 > U71^12
length > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > U811 > U71^12
length > isNatList > U61 > U62 > tt > U92 > U93 > mark1 > U911 > U71^12
length > isNatList > U61 > U62 > tt > U92 > U93 > cons > U911 > U71^12
length > U71 > U72 > s > U21 > tt > nil > mark1 > U811 > U71^12
length > U71 > U72 > s > U21 > tt > nil > mark1 > U911 > U71^12
length > U71 > U72 > s > U21 > tt > U92 > U93 > mark1 > U811 > U71^12
length > U71 > U72 > s > U21 > tt > U92 > U93 > mark1 > U911 > U71^12
length > U71 > U72 > s > U21 > tt > U92 > U93 > cons > U911 > U71^12
length > U71 > U72 > s > isNatIList > U31 > tt > nil > mark1 > U811 > U71^12
length > U71 > U72 > s > isNatIList > U31 > tt > nil > mark1 > U911 > U71^12
length > U71 > U72 > s > isNatIList > U31 > tt > U92 > U93 > mark1 > U811 > U71^12
length > U71 > U72 > s > isNatIList > U31 > tt > U92 > U93 > mark1 > U911 > U71^12
length > U71 > U72 > s > isNatIList > U31 > tt > U92 > U93 > cons > U911 > U71^12
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > nil > mark1 > U811 > U71^12
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > nil > mark1 > U911 > U71^12
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > U811 > U71^12
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > U92 > U93 > mark1 > U911 > U71^12
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > U92 > U93 > cons > U911 > U71^12
U71^12: [2,1]
mark1: [1]
zeros: multiset
cons: []
0: multiset
U11: multiset
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: []
isNatIList: []
U51: []
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
s: multiset
length: []
U811: [1]
nil: multiset
U911: [1]
U92: []
U93: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U711(X1, mark(X2), X3) → U711(X1, X2, X3)
U711(active(X1), X2, X3) → U711(X1, X2, X3)
U711(X1, active(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, active(X3)) → U711(X1, X2, X3)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U711(X1, mark(X2), X3) → U711(X1, X2, X3)
U711(X1, active(X2), X3) → U711(X1, X2, X3)
U711(X1, X2, active(X3)) → U711(X1, X2, X3)
zeros > cons > mark1 > active1
zeros > cons > mark1 > take2
zeros > 0 > tt > nil > mark1 > active1
zeros > 0 > tt > nil > mark1 > take2
zeros > 0 > U81 > nil > mark1 > active1
zeros > 0 > U81 > nil > mark1 > take2
isNatIList > U31 > tt > nil > mark1 > active1
isNatIList > U31 > tt > nil > mark1 > take2
isNatIList > U41 > U42 > tt > nil > mark1 > active1
isNatIList > U41 > U42 > tt > nil > mark1 > take2
isNatIList > isNatList1 > U51 > U52 > tt > nil > mark1 > active1
isNatIList > isNatList1 > U51 > U52 > tt > nil > mark1 > take2
isNatIList > isNatList1 > U611 > U62 > tt > nil > mark1 > active1
isNatIList > isNatList1 > U611 > U62 > tt > nil > mark1 > take2
length > 0 > tt > nil > mark1 > active1
length > 0 > tt > nil > mark1 > take2
length > 0 > U81 > nil > mark1 > active1
length > 0 > U81 > nil > mark1 > take2
length > U11 > tt > nil > mark1 > active1
length > U11 > tt > nil > mark1 > take2
length > isNatList1 > U51 > U52 > tt > nil > mark1 > active1
length > isNatList1 > U51 > U52 > tt > nil > mark1 > take2
length > isNatList1 > U611 > U62 > tt > nil > mark1 > active1
length > isNatList1 > U611 > U62 > tt > nil > mark1 > take2
length > U71 > U72 > s > U21 > tt > nil > mark1 > active1
length > U71 > U72 > s > U21 > tt > nil > mark1 > take2
length > U71 > U72 > s > U91 > U92 > U93 > cons > mark1 > active1
length > U71 > U72 > s > U91 > U92 > U93 > cons > mark1 > take2
U71^12: [2,1]
mark1: [1]
active1: multiset
zeros: multiset
cons: []
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: []
U42: []
isNatIList: []
U51: []
U52: []
isNatList1: [1]
U611: [1]
U62: []
U71: []
U72: multiset
s: multiset
length: []
U81: multiset
nil: multiset
U91: []
U92: []
U93: []
take2: [1,2]
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U711(active(X1), X2, X3) → U711(X1, X2, X3)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U711(active(X1), X2, X3) → U711(X1, X2, X3)
U71^12 > active1
zeros > cons > U41 > U42 > tt > mark1 > active1
zeros > cons > U51 > U52 > tt > mark1 > active1
isNatIList > U31 > tt > mark1 > active1
isNatIList > U41 > U42 > tt > mark1 > active1
isNatIList > isNatList > U51 > U52 > tt > mark1 > active1
isNatIList > isNatList > U61 > U62 > tt > mark1 > active1
isNat1 > U11 > tt > mark1 > active1
isNat1 > U21 > tt > mark1 > active1
isNat1 > isNatList > U51 > U52 > tt > mark1 > active1
isNat1 > isNatList > U61 > U62 > tt > mark1 > active1
length > 0 > U81 > nil > tt > mark1 > active1
length > U11 > tt > mark1 > active1
length > isNatList > U51 > U52 > tt > mark1 > active1
length > isNatList > U61 > U62 > tt > mark1 > active1
length > U71 > U72 > s > U21 > tt > mark1 > active1
take > U61 > U62 > tt > mark1 > active1
take > U81 > nil > tt > mark1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > tt > mark1 > active1
take > U91 > U92 > U93 > cons > U51 > U52 > tt > mark1 > active1
U71^12: multiset
active1: multiset
zeros: multiset
mark1: [1]
cons: []
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: []
U42: []
isNatIList: multiset
U51: []
U52: multiset
isNatList: []
U61: multiset
U62: multiset
U71: []
U72: []
isNat1: [1]
s: []
length: []
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: multiset
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U621(active(X)) → U621(X)
U621(mark(X)) → U621(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U621(active(X)) → U621(X)
U621(mark(X)) → U621(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U611(X1, mark(X2)) → U611(X1, X2)
U611(mark(X1), X2) → U611(X1, X2)
U611(active(X1), X2) → U611(X1, X2)
U611(X1, active(X2)) → U611(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U611(mark(X1), X2) → U611(X1, X2)
U61^11 > cons
zeros > tt > s > mark1 > U811 > cons
zeros > tt > nil > mark1 > U811 > cons
length > 0 > isNatIList > U31 > tt > s > mark1 > U811 > cons
length > 0 > isNatIList > U31 > tt > nil > mark1 > U811 > cons
length > 0 > isNatIList > U41 > U42 > tt > s > mark1 > U811 > cons
length > 0 > isNatIList > U41 > U42 > tt > nil > mark1 > U811 > cons
length > 0 > isNatIList > isNat > U11 > tt > s > mark1 > U811 > cons
length > 0 > isNatIList > isNat > U11 > tt > nil > mark1 > U811 > cons
length > 0 > isNatIList > isNat > U21 > tt > s > mark1 > U811 > cons
length > 0 > isNatIList > isNat > U21 > tt > nil > mark1 > U811 > cons
length > isNatList > U51 > U52 > tt > s > mark1 > U811 > cons
length > isNatList > U51 > U52 > tt > nil > mark1 > U811 > cons
length > isNatList > U61 > isNatIList > U31 > tt > s > mark1 > U811 > cons
length > isNatList > U61 > isNatIList > U31 > tt > nil > mark1 > U811 > cons
length > isNatList > U61 > isNatIList > U41 > U42 > tt > s > mark1 > U811 > cons
length > isNatList > U61 > isNatIList > U41 > U42 > tt > nil > mark1 > U811 > cons
length > isNatList > U61 > isNatIList > isNat > U11 > tt > s > mark1 > U811 > cons
length > isNatList > U61 > isNatIList > isNat > U11 > tt > nil > mark1 > U811 > cons
length > isNatList > U61 > isNatIList > isNat > U21 > tt > s > mark1 > U811 > cons
length > isNatList > U61 > isNatIList > isNat > U21 > tt > nil > mark1 > U811 > cons
length > isNatList > U61 > U62 > tt > s > mark1 > U811 > cons
length > isNatList > U61 > U62 > tt > nil > mark1 > U811 > cons
length > U71 > U72 > s > mark1 > U811 > cons
length > U71 > isNat > U11 > tt > s > mark1 > U811 > cons
length > U71 > isNat > U11 > tt > nil > mark1 > U811 > cons
length > U71 > isNat > U21 > tt > s > mark1 > U811 > cons
length > U71 > isNat > U21 > tt > nil > mark1 > U811 > cons
take > U61 > isNatIList > U31 > tt > s > mark1 > U811 > cons
take > U61 > isNatIList > U31 > tt > nil > mark1 > U811 > cons
take > U61 > isNatIList > U41 > U42 > tt > s > mark1 > U811 > cons
take > U61 > isNatIList > U41 > U42 > tt > nil > mark1 > U811 > cons
take > U61 > isNatIList > isNat > U11 > tt > s > mark1 > U811 > cons
take > U61 > isNatIList > isNat > U11 > tt > nil > mark1 > U811 > cons
take > U61 > isNatIList > isNat > U21 > tt > s > mark1 > U811 > cons
take > U61 > isNatIList > isNat > U21 > tt > nil > mark1 > U811 > cons
take > U61 > U62 > tt > s > mark1 > U811 > cons
take > U61 > U62 > tt > nil > mark1 > U811 > cons
take > U91 > U92 > isNat > U11 > tt > s > mark1 > U811 > cons
take > U91 > U92 > isNat > U11 > tt > nil > mark1 > U811 > cons
take > U91 > U92 > isNat > U21 > tt > s > mark1 > U811 > cons
take > U91 > U92 > isNat > U21 > tt > nil > mark1 > U811 > cons
U61^11: [1]
mark1: multiset
zeros: multiset
cons: []
0: multiset
U11: multiset
tt: multiset
U21: multiset
U31: []
U41: []
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: multiset
U62: []
U71: []
U72: []
isNat: []
s: multiset
length: []
U811: multiset
nil: multiset
U91: []
U92: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U611(X1, mark(X2)) → U611(X1, X2)
U611(active(X1), X2) → U611(X1, X2)
U611(X1, active(X2)) → U611(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U611(X1, mark(X2)) → U611(X1, X2)
U611(X1, active(X2)) → U611(X1, X2)
zeros > 0 > tt > nil > mark1 > active1 > cons
zeros > 0 > tt > nil > mark1 > active1 > U811
length > 0 > tt > nil > mark1 > active1 > cons
length > 0 > tt > nil > mark1 > active1 > U811
length > U11 > tt > nil > mark1 > active1 > cons
length > U11 > tt > nil > mark1 > active1 > U811
length > isNatList1 > U51 > U52 > tt > nil > mark1 > active1 > cons
length > isNatList1 > U51 > U52 > tt > nil > mark1 > active1 > U811
length > U71 > U72 > s > U21 > tt > nil > mark1 > active1 > cons
length > U71 > U72 > s > U21 > tt > nil > mark1 > active1 > U811
length > U71 > U72 > s > U91 > U92 > U93 > mark1 > active1 > cons
length > U71 > U72 > s > U91 > U92 > U93 > mark1 > active1 > U811
take > isNatIList > U31 > tt > nil > mark1 > active1 > cons
take > isNatIList > U31 > tt > nil > mark1 > active1 > U811
take > isNatIList > U41 > U42 > tt > nil > mark1 > active1 > cons
take > isNatIList > U41 > U42 > tt > nil > mark1 > active1 > U811
take > isNatIList > isNatList1 > U51 > U52 > tt > nil > mark1 > active1 > cons
take > isNatIList > isNatList1 > U51 > U52 > tt > nil > mark1 > active1 > U811
take > U61 > U62 > tt > nil > mark1 > active1 > cons
take > U61 > U62 > tt > nil > mark1 > active1 > U811
take > U91 > U92 > U93 > mark1 > active1 > cons
take > U91 > U92 > U93 > mark1 > active1 > U811
mark1: [1]
active1: multiset
zeros: multiset
cons: multiset
0: multiset
U11: multiset
tt: multiset
U21: multiset
U31: []
U41: []
U42: multiset
isNatIList: []
U51: []
U52: multiset
isNatList1: [1]
U61: multiset
U62: []
U71: []
U72: []
s: multiset
length: []
U811: multiset
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U611(active(X1), X2) → U611(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U611(active(X1), X2) → U611(X1, X2)
zeros > cons > U41 > U42 > tt > U72 > mark1 > length1 > active1 > U711
zeros > cons > U41 > U42 > tt > U72 > s > active1 > U711
zeros > cons > isNatList > U51 > U52 > tt > U72 > mark1 > length1 > active1 > U711
zeros > cons > isNatList > U51 > U52 > tt > U72 > s > active1 > U711
zeros > cons > isNatList > U61 > U62 > tt > U72 > mark1 > length1 > active1 > U711
zeros > cons > isNatList > U61 > U62 > tt > U72 > s > active1 > U711
zeros > cons > isNatList > isNat > U11 > tt > U72 > mark1 > length1 > active1 > U711
zeros > cons > isNatList > isNat > U11 > tt > U72 > s > active1 > U711
zeros > cons > isNatList > isNat > U21 > tt > U72 > mark1 > length1 > active1 > U711
zeros > cons > isNatList > isNat > U21 > tt > U72 > s > active1 > U711
zeros > 0 > tt > U72 > mark1 > length1 > active1 > U711
zeros > 0 > tt > U72 > s > active1 > U711
isNatIList1 > U31 > tt > U72 > mark1 > length1 > active1 > U711
isNatIList1 > U31 > tt > U72 > s > active1 > U711
isNatIList1 > U41 > U42 > tt > U72 > mark1 > length1 > active1 > U711
isNatIList1 > U41 > U42 > tt > U72 > s > active1 > U711
isNatIList1 > isNatList > U51 > U52 > tt > U72 > mark1 > length1 > active1 > U711
isNatIList1 > isNatList > U51 > U52 > tt > U72 > s > active1 > U711
isNatIList1 > isNatList > U61 > U62 > tt > U72 > mark1 > length1 > active1 > U711
isNatIList1 > isNatList > U61 > U62 > tt > U72 > s > active1 > U711
isNatIList1 > isNatList > isNat > U11 > tt > U72 > mark1 > length1 > active1 > U711
isNatIList1 > isNatList > isNat > U11 > tt > U72 > s > active1 > U711
isNatIList1 > isNatList > isNat > U21 > tt > U72 > mark1 > length1 > active1 > U711
isNatIList1 > isNatList > isNat > U21 > tt > U72 > s > active1 > U711
take > U81 > nil > 0 > tt > U72 > mark1 > length1 > active1 > U711
take > U81 > nil > 0 > tt > U72 > s > active1 > U711
take > U91 > U92 > U93 > cons > U41 > U42 > tt > U72 > mark1 > length1 > active1 > U711
take > U91 > U92 > U93 > cons > U41 > U42 > tt > U72 > s > active1 > U711
take > U91 > U92 > U93 > cons > isNatList > U51 > U52 > tt > U72 > mark1 > length1 > active1 > U711
take > U91 > U92 > U93 > cons > isNatList > U51 > U52 > tt > U72 > s > active1 > U711
take > U91 > U92 > U93 > cons > isNatList > U61 > U62 > tt > U72 > mark1 > length1 > active1 > U711
take > U91 > U92 > U93 > cons > isNatList > U61 > U62 > tt > U72 > s > active1 > U711
take > U91 > U92 > U93 > cons > isNatList > isNat > U11 > tt > U72 > mark1 > length1 > active1 > U711
take > U91 > U92 > U93 > cons > isNatList > isNat > U11 > tt > U72 > s > active1 > U711
take > U91 > U92 > U93 > cons > isNatList > isNat > U21 > tt > U72 > mark1 > length1 > active1 > U711
take > U91 > U92 > U93 > cons > isNatList > isNat > U21 > tt > U72 > s > active1 > U711
active1: multiset
zeros: multiset
mark1: [1]
cons: []
0: multiset
U11: multiset
tt: multiset
U21: []
U31: []
U41: []
U42: multiset
isNatIList1: [1]
U51: []
U52: multiset
isNatList: []
U61: []
U62: []
U711: [1]
U72: multiset
isNat: multiset
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
ISNATLIST(active(X)) → ISNATLIST(X)
ISNATLIST(mark(X)) → ISNATLIST(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ISNATLIST(active(X)) → ISNATLIST(X)
ISNATLIST(mark(X)) → ISNATLIST(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U521(active(X)) → U521(X)
U521(mark(X)) → U521(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U521(active(X)) → U521(X)
U521(mark(X)) → U521(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U511(X1, mark(X2)) → U511(X1, X2)
U511(mark(X1), X2) → U511(X1, X2)
U511(active(X1), X2) → U511(X1, X2)
U511(X1, active(X2)) → U511(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U511(X1, mark(X2)) → U511(X1, X2)
U511(X1, active(X2)) → U511(X1, X2)
zeros > cons > U51 > U52 > tt > mark1 > active1 > U51^11
zeros > cons > U51 > U52 > tt > mark1 > 0
zeros > cons > U51 > U52 > tt > mark1 > s
isNatIList > U31 > tt > mark1 > active1 > U51^11
isNatIList > U31 > tt > mark1 > 0
isNatIList > U31 > tt > mark1 > s
isNatIList > U41 > U42 > tt > mark1 > active1 > U51^11
isNatIList > U41 > U42 > tt > mark1 > 0
isNatIList > U41 > U42 > tt > mark1 > s
isNatIList > isNat > U11 > tt > mark1 > active1 > U51^11
isNatIList > isNat > U11 > tt > mark1 > 0
isNatIList > isNat > U11 > tt > mark1 > s
isNatIList > isNat > U21 > tt > mark1 > active1 > U51^11
isNatIList > isNat > U21 > tt > mark1 > 0
isNatIList > isNat > U21 > tt > mark1 > s
length > U11 > tt > mark1 > active1 > U51^11
length > U11 > tt > mark1 > 0
length > U11 > tt > mark1 > s
length > U71 > U72 > mark1 > active1 > U51^11
length > U71 > U72 > mark1 > 0
length > U71 > U72 > mark1 > s
take > U61 > U62 > tt > mark1 > active1 > U51^11
take > U61 > U62 > tt > mark1 > 0
take > U61 > U62 > tt > mark1 > s
take > U81 > nil > tt > mark1 > active1 > U51^11
take > U81 > nil > tt > mark1 > 0
take > U81 > nil > tt > mark1 > s
take > U91 > U92 > isNat > U11 > tt > mark1 > active1 > U51^11
take > U91 > U92 > isNat > U11 > tt > mark1 > 0
take > U91 > U92 > isNat > U11 > tt > mark1 > s
take > U91 > U92 > isNat > U21 > tt > mark1 > active1 > U51^11
take > U91 > U92 > isNat > U21 > tt > mark1 > 0
take > U91 > U92 > isNat > U21 > tt > mark1 > s
take > U91 > U92 > U93 > cons > U51 > U52 > tt > mark1 > active1 > U51^11
take > U91 > U92 > U93 > cons > U51 > U52 > tt > mark1 > 0
take > U91 > U92 > U93 > cons > U51 > U52 > tt > mark1 > s
U51^11: multiset
mark1: multiset
active1: multiset
zeros: multiset
cons: []
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: []
U42: []
isNatIList: []
U51: []
U52: []
U61: []
U62: multiset
U71: []
U72: []
isNat: multiset
s: multiset
length: []
U81: []
nil: multiset
U91: []
U92: []
U93: multiset
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U511(mark(X1), X2) → U511(X1, X2)
U511(active(X1), X2) → U511(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U511(mark(X1), X2) → U511(X1, X2)
zeros > cons > mark1
length > 0 > isNatIList > U31 > tt > nil > mark1
length > 0 > isNatIList > U31 > tt > U92 > U93 > cons > mark1
length > 0 > isNatIList > U41 > U42 > tt > nil > mark1
length > 0 > isNatIList > U41 > U42 > tt > U92 > U93 > cons > mark1
length > 0 > isNatIList > isNat > U11 > tt > nil > mark1
length > 0 > isNatIList > isNat > U11 > tt > U92 > U93 > cons > mark1
length > 0 > isNatIList > isNat > U21 > tt > nil > mark1
length > 0 > isNatIList > isNat > U21 > tt > U92 > U93 > cons > mark1
length > 0 > U81 > nil > mark1
length > isNatList > U51 > U52 > tt > nil > mark1
length > isNatList > U51 > U52 > tt > U92 > U93 > cons > mark1
length > isNatList > U61 > isNatIList > U31 > tt > nil > mark1
length > isNatList > U61 > isNatIList > U31 > tt > U92 > U93 > cons > mark1
length > isNatList > U61 > isNatIList > U41 > U42 > tt > nil > mark1
length > isNatList > U61 > isNatIList > U41 > U42 > tt > U92 > U93 > cons > mark1
length > isNatList > U61 > isNatIList > isNat > U11 > tt > nil > mark1
length > isNatList > U61 > isNatIList > isNat > U11 > tt > U92 > U93 > cons > mark1
length > isNatList > U61 > isNatIList > isNat > U21 > tt > nil > mark1
length > isNatList > U61 > isNatIList > isNat > U21 > tt > U92 > U93 > cons > mark1
length > isNatList > U61 > U62 > tt > nil > mark1
length > isNatList > U61 > U62 > tt > U92 > U93 > cons > mark1
length > U71 > U72 > s > isNatIList > U31 > tt > nil > mark1
length > U71 > U72 > s > isNatIList > U31 > tt > U92 > U93 > cons > mark1
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > nil > mark1
length > U71 > U72 > s > isNatIList > U41 > U42 > tt > U92 > U93 > cons > mark1
length > U71 > U72 > s > isNatIList > isNat > U11 > tt > nil > mark1
length > U71 > U72 > s > isNatIList > isNat > U11 > tt > U92 > U93 > cons > mark1
length > U71 > U72 > s > isNatIList > isNat > U21 > tt > nil > mark1
length > U71 > U72 > s > isNatIList > isNat > U21 > tt > U92 > U93 > cons > mark1
length > U71 > U72 > s > U91 > U92 > U93 > cons > mark1
mark1: [1]
zeros: multiset
cons: []
0: multiset
U11: multiset
tt: multiset
U21: []
U31: multiset
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: multiset
s: []
length: []
U81: []
nil: multiset
U91: multiset
U92: multiset
U93: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U511(active(X1), X2) → U511(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U511(active(X1), X2) → U511(X1, X2)
zeros > cons > mark1 > active1 > tt > s
zeros > 0 > mark1 > active1 > tt > s
isNatList1 > U51 > U52 > mark1 > active1 > tt > s
isNatList1 > U61 > U62 > mark1 > active1 > tt > s
isNatList1 > isNat > U11 > mark1 > active1 > tt > s
isNatList1 > isNat > U21 > mark1 > active1 > tt > s
length > 0 > mark1 > active1 > tt > s
length > U11 > mark1 > active1 > tt > s
length > U71 > U72 > mark1 > active1 > tt > s
take > isNatIList > U31 > mark1 > active1 > tt > s
take > isNatIList > U41 > U42 > mark1 > active1 > tt > s
take > isNatIList > isNat > U11 > mark1 > active1 > tt > s
take > isNatIList > isNat > U21 > mark1 > active1 > tt > s
take > U61 > U62 > mark1 > active1 > tt > s
take > U81 > mark1 > active1 > tt > s
take > U81 > nil > active1 > tt > s
take > U91 > U92 > isNat > U11 > mark1 > active1 > tt > s
take > U91 > U92 > isNat > U21 > mark1 > active1 > tt > s
take > U91 > U92 > U93 > cons > mark1 > active1 > tt > s
U51^12: [2,1]
active1: multiset
zeros: multiset
mark1: [1]
cons: []
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: []
U42: multiset
isNatIList: []
U51: []
U52: multiset
isNatList1: multiset
U61: []
U62: multiset
U71: []
U72: []
isNat: multiset
s: []
length: []
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: multiset
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
ISNATILIST(active(X)) → ISNATILIST(X)
ISNATILIST(mark(X)) → ISNATILIST(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ISNATILIST(active(X)) → ISNATILIST(X)
ISNATILIST(mark(X)) → ISNATILIST(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U421(active(X)) → U421(X)
U421(mark(X)) → U421(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U421(active(X)) → U421(X)
U421(mark(X)) → U421(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U411(X1, mark(X2)) → U411(X1, X2)
U411(mark(X1), X2) → U411(X1, X2)
U411(active(X1), X2) → U411(X1, X2)
U411(X1, active(X2)) → U411(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U411(X1, mark(X2)) → U411(X1, X2)
U411(mark(X1), X2) → U411(X1, X2)
U411(active(X1), X2) → U411(X1, X2)
U411(X1, active(X2)) → U411(X1, X2)
U41^12 > U931
zeros > cons > mark1 > active1 > U931
zeros > cons > mark1 > s > U931
isNatIList > U31 > tt > cons > mark1 > active1 > U931
isNatIList > U31 > tt > cons > mark1 > s > U931
isNatIList > U41 > U42 > tt > cons > mark1 > active1 > U931
isNatIList > U41 > U42 > tt > cons > mark1 > s > U931
isNatIList > isNat > U11 > tt > cons > mark1 > active1 > U931
isNatIList > isNat > U11 > tt > cons > mark1 > s > U931
isNatIList > isNat > U21 > tt > cons > mark1 > active1 > U931
isNatIList > isNat > U21 > tt > cons > mark1 > s > U931
isNatList > U51 > U52 > tt > cons > mark1 > active1 > U931
isNatList > U51 > U52 > tt > cons > mark1 > s > U931
isNatList > U61 > U62 > tt > cons > mark1 > active1 > U931
isNatList > U61 > U62 > tt > cons > mark1 > s > U931
isNatList > isNat > U11 > tt > cons > mark1 > active1 > U931
isNatList > isNat > U11 > tt > cons > mark1 > s > U931
isNatList > isNat > U21 > tt > cons > mark1 > active1 > U931
isNatList > isNat > U21 > tt > cons > mark1 > s > U931
length > 0 > U81 > nil > tt > cons > mark1 > active1 > U931
length > 0 > U81 > nil > tt > cons > mark1 > s > U931
length > U11 > tt > cons > mark1 > active1 > U931
length > U11 > tt > cons > mark1 > s > U931
length > U71 > U72 > mark1 > active1 > U931
length > U71 > U72 > mark1 > s > U931
take > U61 > U62 > tt > cons > mark1 > active1 > U931
take > U61 > U62 > tt > cons > mark1 > s > U931
take > U81 > nil > tt > cons > mark1 > active1 > U931
take > U81 > nil > tt > cons > mark1 > s > U931
take > U91 > U92 > isNat > U11 > tt > cons > mark1 > active1 > U931
take > U91 > U92 > isNat > U11 > tt > cons > mark1 > s > U931
take > U91 > U92 > isNat > U21 > tt > cons > mark1 > active1 > U931
take > U91 > U92 > isNat > U21 > tt > cons > mark1 > s > U931
U41^12: [2,1]
mark1: [1]
active1: multiset
zeros: multiset
cons: []
0: multiset
U11: []
tt: multiset
U21: multiset
U31: multiset
U41: multiset
U42: []
isNatIList: []
U51: []
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: multiset
length: []
U81: []
nil: multiset
U91: []
U92: []
U931: [1]
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U311(active(X)) → U311(X)
U311(mark(X)) → U311(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U311(active(X)) → U311(X)
U311(mark(X)) → U311(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U211(active(X)) → U211(X)
U211(mark(X)) → U211(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U211(active(X)) → U211(X)
U211(mark(X)) → U211(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
U111(active(X)) → U111(X)
U111(mark(X)) → U111(X)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
U111(active(X)) → U111(X)
U111(mark(X)) → U111(X)
zeros > cons > U41 > U42 > mark1 > tt > active1
zeros > cons > U41 > U42 > mark1 > length1 > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > tt > active1
zeros > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
zeros > 0 > mark1 > tt > active1
zeros > 0 > mark1 > length1 > active1
isNatIList > U31 > mark1 > tt > active1
isNatIList > U31 > mark1 > length1 > active1
isNatIList > U41 > U42 > mark1 > tt > active1
isNatIList > U41 > U42 > mark1 > length1 > active1
isNatIList > isNatList > U51 > U52 > mark1 > tt > active1
isNatIList > isNatList > U51 > U52 > mark1 > length1 > active1
isNatIList > isNatList > U61 > U62 > mark1 > tt > active1
isNatIList > isNatList > U61 > U62 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U11 > mark1 > tt > active1
isNatIList > isNatList > isNat > U11 > mark1 > length1 > active1
isNatIList > isNatList > isNat > U21 > mark1 > tt > active1
isNatIList > isNatList > isNat > U21 > mark1 > length1 > active1
take > U61 > U62 > mark1 > tt > active1
take > U61 > U62 > mark1 > length1 > active1
take > U81 > nil > 0 > mark1 > tt > active1
take > U81 > nil > 0 > mark1 > length1 > active1
take > U91 > U92 > isNat > U11 > mark1 > tt > active1
take > U91 > U92 > isNat > U11 > mark1 > length1 > active1
take > U91 > U92 > isNat > U21 > mark1 > tt > active1
take > U91 > U92 > isNat > U21 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U41 > U42 > mark1 > length1 > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > tt > active1
take > U91 > U92 > U93 > cons > U71 > U72 > s > U21 > mark1 > length1 > active1
active1: multiset
mark1: [1]
zeros: multiset
cons: multiset
0: multiset
U11: []
tt: multiset
U21: multiset
U31: []
U41: multiset
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
length1: multiset
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
CONS(X1, mark(X2)) → CONS(X1, X2)
CONS(mark(X1), X2) → CONS(X1, X2)
CONS(active(X1), X2) → CONS(X1, X2)
CONS(X1, active(X2)) → CONS(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
CONS(mark(X1), X2) → CONS(X1, X2)
zeros > cons > U71 > U72 > mark1 > 0
zeros > cons > U71 > U72 > mark1 > s
zeros > cons > U71 > U72 > mark1 > U811
isNatList1 > U51 > U52 > tt > cons > U71 > U72 > mark1 > 0
isNatList1 > U51 > U52 > tt > cons > U71 > U72 > mark1 > s
isNatList1 > U51 > U52 > tt > cons > U71 > U72 > mark1 > U811
isNatList1 > U51 > U52 > tt > nil > mark1 > 0
isNatList1 > U51 > U52 > tt > nil > mark1 > s
isNatList1 > U51 > U52 > tt > nil > mark1 > U811
isNatList1 > U61 > U62 > tt > cons > U71 > U72 > mark1 > 0
isNatList1 > U61 > U62 > tt > cons > U71 > U72 > mark1 > s
isNatList1 > U61 > U62 > tt > cons > U71 > U72 > mark1 > U811
isNatList1 > U61 > U62 > tt > nil > mark1 > 0
isNatList1 > U61 > U62 > tt > nil > mark1 > s
isNatList1 > U61 > U62 > tt > nil > mark1 > U811
isNat > U11 > tt > cons > U71 > U72 > mark1 > 0
isNat > U11 > tt > cons > U71 > U72 > mark1 > s
isNat > U11 > tt > cons > U71 > U72 > mark1 > U811
isNat > U11 > tt > nil > mark1 > 0
isNat > U11 > tt > nil > mark1 > s
isNat > U11 > tt > nil > mark1 > U811
isNat > U21 > tt > cons > U71 > U72 > mark1 > 0
isNat > U21 > tt > cons > U71 > U72 > mark1 > s
isNat > U21 > tt > cons > U71 > U72 > mark1 > U811
isNat > U21 > tt > nil > mark1 > 0
isNat > U21 > tt > nil > mark1 > s
isNat > U21 > tt > nil > mark1 > U811
take > isNatIList > U31 > tt > cons > U71 > U72 > mark1 > 0
take > isNatIList > U31 > tt > cons > U71 > U72 > mark1 > s
take > isNatIList > U31 > tt > cons > U71 > U72 > mark1 > U811
take > isNatIList > U31 > tt > nil > mark1 > 0
take > isNatIList > U31 > tt > nil > mark1 > s
take > isNatIList > U31 > tt > nil > mark1 > U811
take > isNatIList > U41 > U42 > tt > cons > U71 > U72 > mark1 > 0
take > isNatIList > U41 > U42 > tt > cons > U71 > U72 > mark1 > s
take > isNatIList > U41 > U42 > tt > cons > U71 > U72 > mark1 > U811
take > isNatIList > U41 > U42 > tt > nil > mark1 > 0
take > isNatIList > U41 > U42 > tt > nil > mark1 > s
take > isNatIList > U41 > U42 > tt > nil > mark1 > U811
take > U61 > U62 > tt > cons > U71 > U72 > mark1 > 0
take > U61 > U62 > tt > cons > U71 > U72 > mark1 > s
take > U61 > U62 > tt > cons > U71 > U72 > mark1 > U811
take > U61 > U62 > tt > nil > mark1 > 0
take > U61 > U62 > tt > nil > mark1 > s
take > U61 > U62 > tt > nil > mark1 > U811
take > U91 > U92 > U93 > cons > U71 > U72 > mark1 > 0
take > U91 > U92 > U93 > cons > U71 > U72 > mark1 > s
take > U91 > U92 > U93 > cons > U71 > U72 > mark1 > U811
mark1: [1]
zeros: multiset
cons: []
0: multiset
U11: []
tt: multiset
U21: []
U31: []
U41: []
U42: multiset
isNatIList: []
U51: multiset
U52: multiset
isNatList1: [1]
U61: []
U62: []
U71: []
U72: []
isNat: []
s: []
U811: multiset
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
CONS(X1, mark(X2)) → CONS(X1, X2)
CONS(active(X1), X2) → CONS(X1, X2)
CONS(X1, active(X2)) → CONS(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
CONS(X1, mark(X2)) → CONS(X1, X2)
CONS(X1, active(X2)) → CONS(X1, X2)
zeros > cons > U51 > U52 > tt > mark1 > active1 > CONS1
zeros > cons > U51 > U52 > tt > mark1 > nil > CONS1
zeros > cons > isNat > U11 > tt > mark1 > active1 > CONS1
zeros > cons > isNat > U11 > tt > mark1 > nil > CONS1
zeros > cons > isNat > U21 > tt > mark1 > active1 > CONS1
zeros > cons > isNat > U21 > tt > mark1 > nil > CONS1
zeros > 0 > tt > mark1 > active1 > CONS1
zeros > 0 > tt > mark1 > nil > CONS1
isNatIList > U31 > tt > mark1 > active1 > CONS1
isNatIList > U31 > tt > mark1 > nil > CONS1
isNatIList > U41 > U42 > tt > mark1 > active1 > CONS1
isNatIList > U41 > U42 > tt > mark1 > nil > CONS1
isNatIList > isNatList > U51 > U52 > tt > mark1 > active1 > CONS1
isNatIList > isNatList > U51 > U52 > tt > mark1 > nil > CONS1
isNatIList > isNatList > U61 > U62 > tt > mark1 > active1 > CONS1
isNatIList > isNatList > U61 > U62 > tt > mark1 > nil > CONS1
isNatIList > isNatList > isNat > U11 > tt > mark1 > active1 > CONS1
isNatIList > isNatList > isNat > U11 > tt > mark1 > nil > CONS1
isNatIList > isNatList > isNat > U21 > tt > mark1 > active1 > CONS1
isNatIList > isNatList > isNat > U21 > tt > mark1 > nil > CONS1
length > 0 > tt > mark1 > active1 > CONS1
length > 0 > tt > mark1 > nil > CONS1
length > isNatList > U51 > U52 > tt > mark1 > active1 > CONS1
length > isNatList > U51 > U52 > tt > mark1 > nil > CONS1
length > isNatList > U61 > U62 > tt > mark1 > active1 > CONS1
length > isNatList > U61 > U62 > tt > mark1 > nil > CONS1
length > isNatList > isNat > U11 > tt > mark1 > active1 > CONS1
length > isNatList > isNat > U11 > tt > mark1 > nil > CONS1
length > isNatList > isNat > U21 > tt > mark1 > active1 > CONS1
length > isNatList > isNat > U21 > tt > mark1 > nil > CONS1
length > U71 > U72 > s > isNat > U11 > tt > mark1 > active1 > CONS1
length > U71 > U72 > s > isNat > U11 > tt > mark1 > nil > CONS1
length > U71 > U72 > s > isNat > U21 > tt > mark1 > active1 > CONS1
length > U71 > U72 > s > isNat > U21 > tt > mark1 > nil > CONS1
take > U61 > U62 > tt > mark1 > active1 > CONS1
take > U61 > U62 > tt > mark1 > nil > CONS1
take > U81 > mark1 > active1 > CONS1
take > U81 > mark1 > nil > CONS1
take > U91 > U92 > U93 > cons > U51 > U52 > tt > mark1 > active1 > CONS1
take > U91 > U92 > U93 > cons > U51 > U52 > tt > mark1 > nil > CONS1
take > U91 > U92 > U93 > cons > isNat > U11 > tt > mark1 > active1 > CONS1
take > U91 > U92 > U93 > cons > isNat > U11 > tt > mark1 > nil > CONS1
take > U91 > U92 > U93 > cons > isNat > U21 > tt > mark1 > active1 > CONS1
take > U91 > U92 > U93 > cons > isNat > U21 > tt > mark1 > nil > CONS1
CONS1: multiset
mark1: [1]
active1: multiset
zeros: multiset
cons: []
0: multiset
U11: multiset
tt: multiset
U21: multiset
U31: []
U41: []
U42: multiset
isNatIList: []
U51: multiset
U52: []
isNatList: []
U61: multiset
U62: []
U71: []
U72: multiset
isNat: []
s: []
length: []
U81: []
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
CONS(active(X1), X2) → CONS(X1, X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
CONS(active(X1), X2) → CONS(X1, X2)
zeros > cons > U51 > U52 > tt > mark1 > active1 > isNatList1
zeros > 0 > U81 > nil > tt > mark1 > active1 > isNatList1
isNatIList > U31 > tt > mark1 > active1 > isNatList1
isNatIList > U41 > U42 > tt > mark1 > active1 > isNatList1
length > 0 > U81 > nil > tt > mark1 > active1 > isNatList1
length > U11 > tt > mark1 > active1 > isNatList1
length > U71 > U72 > s > U21 > tt > mark1 > active1 > isNatList1
length > U71 > U72 > s > U91 > U92 > U93 > cons > U51 > U52 > tt > mark1 > active1 > isNatList1
take > U61 > U62 > tt > mark1 > active1 > isNatList1
take > U81 > nil > tt > mark1 > active1 > isNatList1
take > U91 > U92 > U93 > cons > U51 > U52 > tt > mark1 > active1 > isNatList1
CONS1: multiset
active1: multiset
zeros: multiset
mark1: multiset
cons: multiset
0: multiset
U11: multiset
tt: multiset
U21: []
U31: []
U41: []
U42: multiset
isNatIList: multiset
U51: []
U52: []
isNatList1: multiset
U61: []
U62: []
U71: []
U72: []
s: []
length: []
U81: multiset
nil: multiset
U91: []
U92: []
U93: []
take: []
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)
MARK(cons(X1, X2)) → ACTIVE(cons(mark(X1), X2))
ACTIVE(U41(tt, V2)) → MARK(U42(isNatIList(V2)))
MARK(cons(X1, X2)) → MARK(X1)
MARK(zeros) → ACTIVE(zeros)
ACTIVE(zeros) → MARK(cons(0, zeros))
MARK(U11(X)) → ACTIVE(U11(mark(X)))
ACTIVE(U51(tt, V2)) → MARK(U52(isNatList(V2)))
MARK(U11(X)) → MARK(X)
MARK(U21(X)) → ACTIVE(U21(mark(X)))
ACTIVE(U61(tt, V2)) → MARK(U62(isNatIList(V2)))
MARK(U21(X)) → MARK(X)
MARK(U31(X)) → ACTIVE(U31(mark(X)))
ACTIVE(U71(tt, L, N)) → MARK(U72(isNat(N), L))
MARK(U31(X)) → MARK(X)
MARK(U41(X1, X2)) → ACTIVE(U41(mark(X1), X2))
ACTIVE(U72(tt, L)) → MARK(s(length(L)))
MARK(U41(X1, X2)) → MARK(X1)
MARK(U42(X)) → ACTIVE(U42(mark(X)))
ACTIVE(U91(tt, IL, M, N)) → MARK(U92(isNat(M), IL, M, N))
MARK(U42(X)) → MARK(X)
MARK(isNatIList(X)) → ACTIVE(isNatIList(X))
ACTIVE(U92(tt, IL, M, N)) → MARK(U93(isNat(N), IL, M, N))
MARK(U51(X1, X2)) → ACTIVE(U51(mark(X1), X2))
ACTIVE(U93(tt, IL, M, N)) → MARK(cons(N, take(M, IL)))
MARK(U51(X1, X2)) → MARK(X1)
MARK(U52(X)) → ACTIVE(U52(mark(X)))
ACTIVE(isNat(length(V1))) → MARK(U11(isNatList(V1)))
MARK(U52(X)) → MARK(X)
MARK(isNatList(X)) → ACTIVE(isNatList(X))
ACTIVE(isNat(s(V1))) → MARK(U21(isNat(V1)))
MARK(U61(X1, X2)) → ACTIVE(U61(mark(X1), X2))
ACTIVE(isNatIList(V)) → MARK(U31(isNatList(V)))
MARK(U61(X1, X2)) → MARK(X1)
MARK(U62(X)) → ACTIVE(U62(mark(X)))
ACTIVE(isNatIList(cons(V1, V2))) → MARK(U41(isNat(V1), V2))
MARK(U62(X)) → MARK(X)
MARK(U71(X1, X2, X3)) → ACTIVE(U71(mark(X1), X2, X3))
ACTIVE(isNatList(cons(V1, V2))) → MARK(U51(isNat(V1), V2))
MARK(U71(X1, X2, X3)) → MARK(X1)
MARK(U72(X1, X2)) → ACTIVE(U72(mark(X1), X2))
ACTIVE(isNatList(take(V1, V2))) → MARK(U61(isNat(V1), V2))
MARK(U72(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(length(cons(N, L))) → MARK(U71(isNatList(L), L, N))
MARK(s(X)) → ACTIVE(s(mark(X)))
ACTIVE(take(0, IL)) → MARK(U81(isNatIList(IL)))
MARK(s(X)) → MARK(X)
MARK(length(X)) → ACTIVE(length(mark(X)))
ACTIVE(take(s(M), cons(N, IL))) → MARK(U91(isNatIList(IL), IL, M, N))
MARK(length(X)) → MARK(X)
MARK(U81(X)) → ACTIVE(U81(mark(X)))
MARK(U81(X)) → MARK(X)
MARK(U91(X1, X2, X3, X4)) → ACTIVE(U91(mark(X1), X2, X3, X4))
MARK(U91(X1, X2, X3, X4)) → MARK(X1)
MARK(U92(X1, X2, X3, X4)) → ACTIVE(U92(mark(X1), X2, X3, X4))
MARK(U92(X1, X2, X3, X4)) → MARK(X1)
MARK(U93(X1, X2, X3, X4)) → ACTIVE(U93(mark(X1), X2, X3, X4))
MARK(U93(X1, X2, X3, X4)) → MARK(X1)
MARK(take(X1, X2)) → ACTIVE(take(mark(X1), mark(X2)))
MARK(take(X1, X2)) → MARK(X1)
MARK(take(X1, X2)) → MARK(X2)
active(zeros) → mark(cons(0, zeros))
active(U11(tt)) → mark(tt)
active(U21(tt)) → mark(tt)
active(U31(tt)) → mark(tt)
active(U41(tt, V2)) → mark(U42(isNatIList(V2)))
active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isNatList(V2)))
active(U52(tt)) → mark(tt)
active(U61(tt, V2)) → mark(U62(isNatIList(V2)))
active(U62(tt)) → mark(tt)
active(U71(tt, L, N)) → mark(U72(isNat(N), L))
active(U72(tt, L)) → mark(s(length(L)))
active(U81(tt)) → mark(nil)
active(U91(tt, IL, M, N)) → mark(U92(isNat(M), IL, M, N))
active(U92(tt, IL, M, N)) → mark(U93(isNat(N), IL, M, N))
active(U93(tt, IL, M, N)) → mark(cons(N, take(M, IL)))
active(isNat(0)) → mark(tt)
active(isNat(length(V1))) → mark(U11(isNatList(V1)))
active(isNat(s(V1))) → mark(U21(isNat(V1)))
active(isNatIList(V)) → mark(U31(isNatList(V)))
active(isNatIList(zeros)) → mark(tt)
active(isNatIList(cons(V1, V2))) → mark(U41(isNat(V1), V2))
active(isNatList(nil)) → mark(tt)
active(isNatList(cons(V1, V2))) → mark(U51(isNat(V1), V2))
active(isNatList(take(V1, V2))) → mark(U61(isNat(V1), V2))
active(length(nil)) → mark(0)
active(length(cons(N, L))) → mark(U71(isNatList(L), L, N))
active(take(0, IL)) → mark(U81(isNatIList(IL)))
active(take(s(M), cons(N, IL))) → mark(U91(isNatIList(IL), IL, M, N))
mark(zeros) → active(zeros)
mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(0) → active(0)
mark(U11(X)) → active(U11(mark(X)))
mark(tt) → active(tt)
mark(U21(X)) → active(U21(mark(X)))
mark(U31(X)) → active(U31(mark(X)))
mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))
mark(isNatIList(X)) → active(isNatIList(X))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))
mark(isNatList(X)) → active(isNatList(X))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(U71(X1, X2, X3)) → active(U71(mark(X1), X2, X3))
mark(U72(X1, X2)) → active(U72(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(s(X)) → active(s(mark(X)))
mark(length(X)) → active(length(mark(X)))
mark(U81(X)) → active(U81(mark(X)))
mark(nil) → active(nil)
mark(U91(X1, X2, X3, X4)) → active(U91(mark(X1), X2, X3, X4))
mark(U92(X1, X2, X3, X4)) → active(U92(mark(X1), X2, X3, X4))
mark(U93(X1, X2, X3, X4)) → active(U93(mark(X1), X2, X3, X4))
mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
cons(mark(X1), X2) → cons(X1, X2)
cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)
cons(X1, active(X2)) → cons(X1, X2)
U11(mark(X)) → U11(X)
U11(active(X)) → U11(X)
U21(mark(X)) → U21(X)
U21(active(X)) → U21(X)
U31(mark(X)) → U31(X)
U31(active(X)) → U31(X)
U41(mark(X1), X2) → U41(X1, X2)
U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)
U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)
U42(active(X)) → U42(X)
isNatIList(mark(X)) → isNatIList(X)
isNatIList(active(X)) → isNatIList(X)
U51(mark(X1), X2) → U51(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)
U52(active(X)) → U52(X)
isNatList(mark(X)) → isNatList(X)
isNatList(active(X)) → isNatList(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(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, mark(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, mark(X3)) → U71(X1, X2, X3)
U71(active(X1), X2, X3) → U71(X1, X2, X3)
U71(X1, active(X2), X3) → U71(X1, X2, X3)
U71(X1, X2, active(X3)) → U71(X1, X2, X3)
U72(mark(X1), X2) → U72(X1, X2)
U72(X1, mark(X2)) → U72(X1, X2)
U72(active(X1), X2) → U72(X1, X2)
U72(X1, active(X2)) → U72(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
s(mark(X)) → s(X)
s(active(X)) → s(X)
length(mark(X)) → length(X)
length(active(X)) → length(X)
U81(mark(X)) → U81(X)
U81(active(X)) → U81(X)
U91(mark(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, mark(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, mark(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, mark(X4)) → U91(X1, X2, X3, X4)
U91(active(X1), X2, X3, X4) → U91(X1, X2, X3, X4)
U91(X1, active(X2), X3, X4) → U91(X1, X2, X3, X4)
U91(X1, X2, active(X3), X4) → U91(X1, X2, X3, X4)
U91(X1, X2, X3, active(X4)) → U91(X1, X2, X3, X4)
U92(mark(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, mark(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, mark(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, mark(X4)) → U92(X1, X2, X3, X4)
U92(active(X1), X2, X3, X4) → U92(X1, X2, X3, X4)
U92(X1, active(X2), X3, X4) → U92(X1, X2, X3, X4)
U92(X1, X2, active(X3), X4) → U92(X1, X2, X3, X4)
U92(X1, X2, X3, active(X4)) → U92(X1, X2, X3, X4)
U93(mark(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, mark(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, mark(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, mark(X4)) → U93(X1, X2, X3, X4)
U93(active(X1), X2, X3, X4) → U93(X1, X2, X3, X4)
U93(X1, active(X2), X3, X4) → U93(X1, X2, X3, X4)
U93(X1, X2, active(X3), X4) → U93(X1, X2, X3, X4)
U93(X1, X2, X3, active(X4)) → U93(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)