0 QTRS
↳1 DependencyPairsProof (⇔)
↳2 QDP
↳3 DependencyGraphProof (⇔)
↳4 AND
↳5 QDP
↳6 UsableRulesProof (⇔)
↳7 QDP
↳8 QDPSizeChangeProof (⇔)
↳9 TRUE
↳10 QDP
↳11 UsableRulesProof (⇔)
↳12 QDP
↳13 QDPSizeChangeProof (⇔)
↳14 TRUE
↳15 QDP
↳16 UsableRulesProof (⇔)
↳17 QDP
↳18 QDPSizeChangeProof (⇔)
↳19 TRUE
↳20 QDP
↳21 UsableRulesProof (⇔)
↳22 QDP
↳23 QDPSizeChangeProof (⇔)
↳24 TRUE
↳25 QDP
↳26 UsableRulesProof (⇔)
↳27 QDP
↳28 QDPSizeChangeProof (⇔)
↳29 TRUE
↳30 QDP
↳31 UsableRulesProof (⇔)
↳32 QDP
↳33 QDPSizeChangeProof (⇔)
↳34 TRUE
↳35 QDP
↳36 UsableRulesProof (⇔)
↳37 QDP
↳38 QDPSizeChangeProof (⇔)
↳39 TRUE
↳40 QDP
↳41 UsableRulesProof (⇔)
↳42 QDP
↳43 QDPSizeChangeProof (⇔)
↳44 TRUE
↳45 QDP
↳46 UsableRulesProof (⇔)
↳47 QDP
↳48 QDPSizeChangeProof (⇔)
↳49 TRUE
↳50 QDP
↳51 UsableRulesProof (⇔)
↳52 QDP
↳53 QDPSizeChangeProof (⇔)
↳54 TRUE
↳55 QDP
↳56 UsableRulesProof (⇔)
↳57 QDP
↳58 QDPSizeChangeProof (⇔)
↳59 TRUE
↳60 QDP
↳61 UsableRulesProof (⇔)
↳62 QDP
↳63 QDPSizeChangeProof (⇔)
↳64 TRUE
↳65 QDP
↳66 UsableRulesProof (⇔)
↳67 QDP
↳68 QDPSizeChangeProof (⇔)
↳69 TRUE
↳70 QDP
↳71 UsableRulesProof (⇔)
↳72 QDP
↳73 QDPSizeChangeProof (⇔)
↳74 TRUE
↳75 QDP
↳76 UsableRulesProof (⇔)
↳77 QDP
↳78 QDPSizeChangeProof (⇔)
↳79 TRUE
↳80 QDP
↳81 UsableRulesProof (⇔)
↳82 QDP
↳83 QDPSizeChangeProof (⇔)
↳84 TRUE
↳85 QDP
↳86 UsableRulesProof (⇔)
↳87 QDP
↳88 QDPSizeChangeProof (⇔)
↳89 TRUE
↳90 QDP
↳91 UsableRulesProof (⇔)
↳92 QDP
↳93 QDPSizeChangeProof (⇔)
↳94 TRUE
↳95 QDP
↳96 UsableRulesProof (⇔)
↳97 QDP
↳98 QDPSizeChangeProof (⇔)
↳99 TRUE
↳100 QDP
↳101 UsableRulesProof (⇔)
↳102 QDP
↳103 QDPSizeChangeProof (⇔)
↳104 TRUE
↳105 QDP
↳106 UsableRulesProof (⇔)
↳107 QDP
↳108 QDPSizeChangeProof (⇔)
↳109 TRUE
↳110 QDP
↳111 UsableRulesProof (⇔)
↳112 QDP
↳113 QDPSizeChangeProof (⇔)
↳114 TRUE
↳115 QDP
↳116 QDPOrderProof (⇔)
↳117 QDP
↳118 QDPOrderProof (⇔)
↳119 QDP
↳120 QDPOrderProof (⇔)
↳121 QDP
↳122 QDPOrderProof (⇔)
↳123 QDP
↳124 QDPOrderProof (⇔)
↳125 QDP
↳126 QDPOrderProof (⇔)
↳127 QDP
↳128 QDPOrderProof (⇔)
↳129 QDP
↳130 QDPOrderProof (⇔)
↳131 QDP
↳132 QDPOrderProof (⇔)
↳133 QDP
↳134 QDPOrderProof (⇔)
↳135 QDP
↳136 QDPOrderProof (⇔)
↳137 QDP
↳138 QDPOrderProof (⇔)
↳139 QDP
↳140 QDPOrderProof (⇔)
↳141 QDP
↳142 QDPOrderProof (⇔)
↳143 QDP
↳144 QDPOrderProof (⇔)
↳145 QDP
↳146 QDPOrderProof (⇔)
↳147 QDP
↳148 QDPOrderProof (⇔)
↳149 QDP
↳150 QDPOrderProof (⇔)
↳151 QDP
↳152 QDPOrderProof (⇔)
↳153 QDP
↳154 QDPOrderProof (⇔)
↳155 QDP
↳156 QDPOrderProof (⇔)
↳157 QDP
↳158 QDPOrderProof (⇔)
↳159 QDP
↳160 QDPOrderProof (⇔)
↳161 QDP
↳162 QDPOrderProof (⇔)
↳163 QDP
↳164 QDPOrderProof (⇔)
↳165 QDP
↳166 QDPOrderProof (⇔)
↳167 QDP
↳168 QDPOrderProof (⇔)
↳169 QDP
↳170 QDPOrderProof (⇔)
↳171 QDP
↳172 QDPOrderProof (⇔)
↳173 QDP
↳174 QDPOrderProof (⇔)
↳175 QDP
↳176 QDPOrderProof (⇔)
↳177 QDP
↳178 QDPOrderProof (⇔)
↳179 QDP
↳180 QDPOrderProof (⇔)
↳181 QDP
↳182 QDPOrderProof (⇔)
↳183 QDP
↳184 QDPOrderProof (⇔)
↳185 QDP
↳186 QDPOrderProof (⇔)
↳187 QDP
↳188 QDPOrderProof (⇔)
↳189 QDP
↳190 QDPOrderProof (⇔)
↳191 QDP
↳192 QDPOrderProof (⇔)
↳193 QDP
↳194 QDPOrderProof (⇔)
↳195 QDP
↳196 QDPOrderProof (⇔)
↳197 QDP
↳198 DependencyGraphProof (⇔)
↳199 QDP
↳200 UsableRulesProof (⇔)
↳201 QDP
↳202 QDPSizeChangeProof (⇔)
↳203 TRUE
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
ACTIVE(U11(tt, V1, V2)) → U121(isNatKind(V1), V1, V2)
ACTIVE(U11(tt, V1, V2)) → ISNATKIND(V1)
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
ACTIVE(U12(tt, V1, V2)) → U131(isNatKind(V2), V1, V2)
ACTIVE(U12(tt, V1, V2)) → ISNATKIND(V2)
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
ACTIVE(U13(tt, V1, V2)) → U141(isNatKind(V2), V1, V2)
ACTIVE(U13(tt, V1, V2)) → ISNATKIND(V2)
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
ACTIVE(U14(tt, V1, V2)) → U151(isNat(V1), V2)
ACTIVE(U14(tt, V1, V2)) → ISNAT(V1)
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
ACTIVE(U15(tt, V2)) → U161(isNat(V2))
ACTIVE(U15(tt, V2)) → ISNAT(V2)
ACTIVE(U16(tt)) → MARK(tt)
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
ACTIVE(U21(tt, V1)) → U221(isNatKind(V1), V1)
ACTIVE(U21(tt, V1)) → ISNATKIND(V1)
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U22(tt, V1)) → U231(isNat(V1))
ACTIVE(U22(tt, V1)) → ISNAT(V1)
ACTIVE(U23(tt)) → MARK(tt)
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
ACTIVE(U31(tt, V2)) → U321(isNatKind(V2))
ACTIVE(U31(tt, V2)) → ISNATKIND(V2)
ACTIVE(U32(tt)) → MARK(tt)
ACTIVE(U41(tt)) → MARK(tt)
ACTIVE(U51(tt, N)) → MARK(U52(isNatKind(N), N))
ACTIVE(U51(tt, N)) → U521(isNatKind(N), N)
ACTIVE(U51(tt, N)) → ISNATKIND(N)
ACTIVE(U52(tt, N)) → MARK(N)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
ACTIVE(U61(tt, M, N)) → U621(isNatKind(M), M, N)
ACTIVE(U61(tt, M, N)) → ISNATKIND(M)
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
ACTIVE(U62(tt, M, N)) → U631(isNat(N), M, N)
ACTIVE(U62(tt, M, N)) → ISNAT(N)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U63(tt, M, N)) → U641(isNatKind(N), M, N)
ACTIVE(U63(tt, M, N)) → ISNATKIND(N)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
ACTIVE(U64(tt, M, N)) → S(plus(N, M))
ACTIVE(U64(tt, M, N)) → PLUS(N, M)
ACTIVE(isNat(0)) → MARK(tt)
ACTIVE(isNat(plus(V1, V2))) → MARK(U11(isNatKind(V1), V1, V2))
ACTIVE(isNat(plus(V1, V2))) → U111(isNatKind(V1), V1, V2)
ACTIVE(isNat(plus(V1, V2))) → ISNATKIND(V1)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNat(s(V1))) → U211(isNatKind(V1), V1)
ACTIVE(isNat(s(V1))) → ISNATKIND(V1)
ACTIVE(isNatKind(0)) → MARK(tt)
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
ACTIVE(isNatKind(plus(V1, V2))) → U311(isNatKind(V1), V2)
ACTIVE(isNatKind(plus(V1, V2))) → ISNATKIND(V1)
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
ACTIVE(isNatKind(s(V1))) → U411(isNatKind(V1))
ACTIVE(isNatKind(s(V1))) → ISNATKIND(V1)
ACTIVE(plus(N, 0)) → MARK(U51(isNat(N), N))
ACTIVE(plus(N, 0)) → U511(isNat(N), N)
ACTIVE(plus(N, 0)) → ISNAT(N)
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
ACTIVE(plus(N, s(M))) → U611(isNat(M), M, N)
ACTIVE(plus(N, s(M))) → ISNAT(M)
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
MARK(U11(X1, X2, X3)) → U111(mark(X1), X2, X3)
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(tt) → ACTIVE(tt)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
MARK(U12(X1, X2, X3)) → U121(mark(X1), X2, X3)
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
MARK(U13(X1, X2, X3)) → U131(mark(X1), X2, X3)
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
MARK(U14(X1, X2, X3)) → U141(mark(X1), X2, X3)
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
MARK(U15(X1, X2)) → U151(mark(X1), X2)
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
MARK(U16(X)) → ACTIVE(U16(mark(X)))
MARK(U16(X)) → U161(mark(X))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → U211(mark(X1), X2)
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → U221(mark(X1), X2)
MARK(U22(X1, X2)) → MARK(X1)
MARK(U23(X)) → ACTIVE(U23(mark(X)))
MARK(U23(X)) → U231(mark(X))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
MARK(U31(X1, X2)) → U311(mark(X1), X2)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X)) → ACTIVE(U32(mark(X)))
MARK(U32(X)) → U321(mark(X))
MARK(U32(X)) → MARK(X)
MARK(U41(X)) → ACTIVE(U41(mark(X)))
MARK(U41(X)) → U411(mark(X))
MARK(U41(X)) → MARK(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(X1, X2)) → ACTIVE(U52(mark(X1), X2))
MARK(U52(X1, X2)) → U521(mark(X1), X2)
MARK(U52(X1, X2)) → MARK(X1)
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
MARK(U61(X1, X2, X3)) → U611(mark(X1), X2, X3)
MARK(U61(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
MARK(U62(X1, X2, X3)) → U621(mark(X1), X2, X3)
MARK(U62(X1, X2, X3)) → MARK(X1)
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U63(X1, X2, X3)) → U631(mark(X1), X2, X3)
MARK(U63(X1, X2, X3)) → MARK(X1)
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → U641(mark(X1), X2, X3)
MARK(U64(X1, X2, X3)) → MARK(X1)
MARK(s(X)) → ACTIVE(s(mark(X)))
MARK(s(X)) → S(mark(X))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
MARK(plus(X1, X2)) → PLUS(mark(X1), mark(X2))
MARK(plus(X1, X2)) → MARK(X1)
MARK(plus(X1, X2)) → MARK(X2)
MARK(0) → ACTIVE(0)
U111(mark(X1), X2, X3) → U111(X1, X2, X3)
U111(X1, mark(X2), X3) → U111(X1, X2, X3)
U111(X1, X2, mark(X3)) → U111(X1, X2, X3)
U111(active(X1), X2, X3) → U111(X1, X2, X3)
U111(X1, active(X2), X3) → U111(X1, X2, X3)
U111(X1, X2, active(X3)) → U111(X1, X2, X3)
U121(mark(X1), X2, X3) → U121(X1, X2, X3)
U121(X1, mark(X2), X3) → U121(X1, X2, X3)
U121(X1, X2, mark(X3)) → U121(X1, X2, X3)
U121(active(X1), X2, X3) → U121(X1, X2, X3)
U121(X1, active(X2), X3) → U121(X1, X2, X3)
U121(X1, X2, active(X3)) → U121(X1, X2, X3)
ISNATKIND(mark(X)) → ISNATKIND(X)
ISNATKIND(active(X)) → ISNATKIND(X)
U131(mark(X1), X2, X3) → U131(X1, X2, X3)
U131(X1, mark(X2), X3) → U131(X1, X2, X3)
U131(X1, X2, mark(X3)) → U131(X1, X2, X3)
U131(active(X1), X2, X3) → U131(X1, X2, X3)
U131(X1, active(X2), X3) → U131(X1, X2, X3)
U131(X1, X2, active(X3)) → U131(X1, X2, X3)
U141(mark(X1), X2, X3) → U141(X1, X2, X3)
U141(X1, mark(X2), X3) → U141(X1, X2, X3)
U141(X1, X2, mark(X3)) → U141(X1, X2, X3)
U141(active(X1), X2, X3) → U141(X1, X2, X3)
U141(X1, active(X2), X3) → U141(X1, X2, X3)
U141(X1, X2, active(X3)) → U141(X1, X2, X3)
U151(mark(X1), X2) → U151(X1, X2)
U151(X1, mark(X2)) → U151(X1, X2)
U151(active(X1), X2) → U151(X1, X2)
U151(X1, active(X2)) → U151(X1, X2)
ISNAT(mark(X)) → ISNAT(X)
ISNAT(active(X)) → ISNAT(X)
U161(mark(X)) → U161(X)
U161(active(X)) → U161(X)
U211(mark(X1), X2) → U211(X1, X2)
U211(X1, mark(X2)) → U211(X1, X2)
U211(active(X1), X2) → U211(X1, X2)
U211(X1, active(X2)) → U211(X1, X2)
U221(mark(X1), X2) → U221(X1, X2)
U221(X1, mark(X2)) → U221(X1, X2)
U221(active(X1), X2) → U221(X1, X2)
U221(X1, active(X2)) → U221(X1, X2)
U231(mark(X)) → U231(X)
U231(active(X)) → U231(X)
U311(mark(X1), X2) → U311(X1, X2)
U311(X1, mark(X2)) → U311(X1, X2)
U311(active(X1), X2) → U311(X1, X2)
U311(X1, active(X2)) → U311(X1, X2)
U321(mark(X)) → U321(X)
U321(active(X)) → U321(X)
U411(mark(X)) → U411(X)
U411(active(X)) → U411(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(X1), X2) → U521(X1, X2)
U521(X1, mark(X2)) → U521(X1, X2)
U521(active(X1), X2) → U521(X1, X2)
U521(X1, active(X2)) → U521(X1, X2)
U611(mark(X1), X2, X3) → U611(X1, X2, X3)
U611(X1, mark(X2), X3) → U611(X1, X2, X3)
U611(X1, X2, mark(X3)) → U611(X1, X2, X3)
U611(active(X1), X2, X3) → U611(X1, X2, X3)
U611(X1, active(X2), X3) → U611(X1, X2, X3)
U611(X1, X2, active(X3)) → U611(X1, X2, X3)
U621(mark(X1), X2, X3) → U621(X1, X2, X3)
U621(X1, mark(X2), X3) → U621(X1, X2, X3)
U621(X1, X2, mark(X3)) → U621(X1, X2, X3)
U621(active(X1), X2, X3) → U621(X1, X2, X3)
U621(X1, active(X2), X3) → U621(X1, X2, X3)
U621(X1, X2, active(X3)) → U621(X1, X2, X3)
U631(mark(X1), X2, X3) → U631(X1, X2, X3)
U631(X1, mark(X2), X3) → U631(X1, X2, X3)
U631(X1, X2, mark(X3)) → U631(X1, X2, X3)
U631(active(X1), X2, X3) → U631(X1, X2, X3)
U631(X1, active(X2), X3) → U631(X1, X2, X3)
U631(X1, X2, active(X3)) → U631(X1, X2, X3)
U641(mark(X1), X2, X3) → U641(X1, X2, X3)
U641(X1, mark(X2), X3) → U641(X1, X2, X3)
U641(X1, X2, mark(X3)) → U641(X1, X2, X3)
U641(active(X1), X2, X3) → U641(X1, X2, X3)
U641(X1, active(X2), X3) → U641(X1, X2, X3)
U641(X1, X2, active(X3)) → U641(X1, X2, X3)
S(mark(X)) → S(X)
S(active(X)) → S(X)
PLUS(mark(X1), X2) → PLUS(X1, X2)
PLUS(X1, mark(X2)) → PLUS(X1, X2)
PLUS(active(X1), X2) → PLUS(X1, X2)
PLUS(X1, active(X2)) → PLUS(X1, X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
PLUS(X1, mark(X2)) → PLUS(X1, X2)
PLUS(mark(X1), X2) → PLUS(X1, X2)
PLUS(active(X1), X2) → PLUS(X1, X2)
PLUS(X1, active(X2)) → PLUS(X1, X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
PLUS(X1, mark(X2)) → PLUS(X1, X2)
PLUS(mark(X1), X2) → PLUS(X1, X2)
PLUS(active(X1), X2) → PLUS(X1, X2)
PLUS(X1, active(X2)) → PLUS(X1, X2)
From the DPs we obtained the following set of size-change graphs:
S(active(X)) → S(X)
S(mark(X)) → S(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
S(active(X)) → S(X)
S(mark(X)) → S(X)
From the DPs we obtained the following set of size-change graphs:
U641(X1, mark(X2), X3) → U641(X1, X2, X3)
U641(mark(X1), X2, X3) → U641(X1, X2, X3)
U641(X1, X2, mark(X3)) → U641(X1, X2, X3)
U641(active(X1), X2, X3) → U641(X1, X2, X3)
U641(X1, active(X2), X3) → U641(X1, X2, X3)
U641(X1, X2, active(X3)) → U641(X1, X2, X3)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U641(X1, mark(X2), X3) → U641(X1, X2, X3)
U641(mark(X1), X2, X3) → U641(X1, X2, X3)
U641(X1, X2, mark(X3)) → U641(X1, X2, X3)
U641(active(X1), X2, X3) → U641(X1, X2, X3)
U641(X1, active(X2), X3) → U641(X1, X2, X3)
U641(X1, X2, active(X3)) → U641(X1, X2, X3)
From the DPs we obtained the following set of size-change graphs:
U631(X1, mark(X2), X3) → U631(X1, X2, X3)
U631(mark(X1), X2, X3) → U631(X1, X2, X3)
U631(X1, X2, mark(X3)) → U631(X1, X2, X3)
U631(active(X1), X2, X3) → U631(X1, X2, X3)
U631(X1, active(X2), X3) → U631(X1, X2, X3)
U631(X1, X2, active(X3)) → U631(X1, X2, X3)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U631(X1, mark(X2), X3) → U631(X1, X2, X3)
U631(mark(X1), X2, X3) → U631(X1, X2, X3)
U631(X1, X2, mark(X3)) → U631(X1, X2, X3)
U631(active(X1), X2, X3) → U631(X1, X2, X3)
U631(X1, active(X2), X3) → U631(X1, X2, X3)
U631(X1, X2, active(X3)) → U631(X1, X2, X3)
From the DPs we obtained the following set of size-change graphs:
U621(X1, mark(X2), X3) → U621(X1, X2, X3)
U621(mark(X1), X2, X3) → U621(X1, X2, X3)
U621(X1, X2, mark(X3)) → U621(X1, X2, X3)
U621(active(X1), X2, X3) → U621(X1, X2, X3)
U621(X1, active(X2), X3) → U621(X1, X2, X3)
U621(X1, X2, active(X3)) → U621(X1, X2, X3)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U621(X1, mark(X2), X3) → U621(X1, X2, X3)
U621(mark(X1), X2, X3) → U621(X1, X2, X3)
U621(X1, X2, mark(X3)) → U621(X1, X2, X3)
U621(active(X1), X2, X3) → U621(X1, X2, X3)
U621(X1, active(X2), X3) → U621(X1, X2, X3)
U621(X1, X2, active(X3)) → U621(X1, X2, X3)
From the DPs we obtained the following set of size-change graphs:
U611(X1, mark(X2), X3) → U611(X1, X2, X3)
U611(mark(X1), X2, X3) → U611(X1, X2, X3)
U611(X1, X2, mark(X3)) → U611(X1, X2, X3)
U611(active(X1), X2, X3) → U611(X1, X2, X3)
U611(X1, active(X2), X3) → U611(X1, X2, X3)
U611(X1, X2, active(X3)) → U611(X1, X2, X3)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U611(X1, mark(X2), X3) → U611(X1, X2, X3)
U611(mark(X1), X2, X3) → U611(X1, X2, X3)
U611(X1, X2, mark(X3)) → U611(X1, X2, X3)
U611(active(X1), X2, X3) → U611(X1, X2, X3)
U611(X1, active(X2), X3) → U611(X1, X2, X3)
U611(X1, X2, active(X3)) → U611(X1, X2, X3)
From the DPs we obtained the following set of size-change graphs:
U521(X1, mark(X2)) → U521(X1, X2)
U521(mark(X1), X2) → U521(X1, X2)
U521(active(X1), X2) → U521(X1, X2)
U521(X1, active(X2)) → U521(X1, X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U521(X1, mark(X2)) → U521(X1, X2)
U521(mark(X1), X2) → U521(X1, X2)
U521(active(X1), X2) → U521(X1, X2)
U521(X1, active(X2)) → U521(X1, X2)
From the DPs we obtained the following set of size-change graphs:
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(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(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)
From the DPs we obtained the following set of size-change graphs:
U411(active(X)) → U411(X)
U411(mark(X)) → U411(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U411(active(X)) → U411(X)
U411(mark(X)) → U411(X)
From the DPs we obtained the following set of size-change graphs:
U321(active(X)) → U321(X)
U321(mark(X)) → U321(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U321(active(X)) → U321(X)
U321(mark(X)) → U321(X)
From the DPs we obtained the following set of size-change graphs:
U311(X1, mark(X2)) → U311(X1, X2)
U311(mark(X1), X2) → U311(X1, X2)
U311(active(X1), X2) → U311(X1, X2)
U311(X1, active(X2)) → U311(X1, X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U311(X1, mark(X2)) → U311(X1, X2)
U311(mark(X1), X2) → U311(X1, X2)
U311(active(X1), X2) → U311(X1, X2)
U311(X1, active(X2)) → U311(X1, X2)
From the DPs we obtained the following set of size-change graphs:
U231(active(X)) → U231(X)
U231(mark(X)) → U231(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U231(active(X)) → U231(X)
U231(mark(X)) → U231(X)
From the DPs we obtained the following set of size-change graphs:
U221(X1, mark(X2)) → U221(X1, X2)
U221(mark(X1), X2) → U221(X1, X2)
U221(active(X1), X2) → U221(X1, X2)
U221(X1, active(X2)) → U221(X1, X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U221(X1, mark(X2)) → U221(X1, X2)
U221(mark(X1), X2) → U221(X1, X2)
U221(active(X1), X2) → U221(X1, X2)
U221(X1, active(X2)) → U221(X1, X2)
From the DPs we obtained the following set of size-change graphs:
U211(X1, mark(X2)) → U211(X1, X2)
U211(mark(X1), X2) → U211(X1, X2)
U211(active(X1), X2) → U211(X1, X2)
U211(X1, active(X2)) → U211(X1, X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U211(X1, mark(X2)) → U211(X1, X2)
U211(mark(X1), X2) → U211(X1, X2)
U211(active(X1), X2) → U211(X1, X2)
U211(X1, active(X2)) → U211(X1, X2)
From the DPs we obtained the following set of size-change graphs:
U161(active(X)) → U161(X)
U161(mark(X)) → U161(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U161(active(X)) → U161(X)
U161(mark(X)) → U161(X)
From the DPs we obtained the following set of size-change graphs:
ISNAT(active(X)) → ISNAT(X)
ISNAT(mark(X)) → ISNAT(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
ISNAT(active(X)) → ISNAT(X)
ISNAT(mark(X)) → ISNAT(X)
From the DPs we obtained the following set of size-change graphs:
U151(X1, mark(X2)) → U151(X1, X2)
U151(mark(X1), X2) → U151(X1, X2)
U151(active(X1), X2) → U151(X1, X2)
U151(X1, active(X2)) → U151(X1, X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U151(X1, mark(X2)) → U151(X1, X2)
U151(mark(X1), X2) → U151(X1, X2)
U151(active(X1), X2) → U151(X1, X2)
U151(X1, active(X2)) → U151(X1, X2)
From the DPs we obtained the following set of size-change graphs:
U141(X1, mark(X2), X3) → U141(X1, X2, X3)
U141(mark(X1), X2, X3) → U141(X1, X2, X3)
U141(X1, X2, mark(X3)) → U141(X1, X2, X3)
U141(active(X1), X2, X3) → U141(X1, X2, X3)
U141(X1, active(X2), X3) → U141(X1, X2, X3)
U141(X1, X2, active(X3)) → U141(X1, X2, X3)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U141(X1, mark(X2), X3) → U141(X1, X2, X3)
U141(mark(X1), X2, X3) → U141(X1, X2, X3)
U141(X1, X2, mark(X3)) → U141(X1, X2, X3)
U141(active(X1), X2, X3) → U141(X1, X2, X3)
U141(X1, active(X2), X3) → U141(X1, X2, X3)
U141(X1, X2, active(X3)) → U141(X1, X2, X3)
From the DPs we obtained the following set of size-change graphs:
U131(X1, mark(X2), X3) → U131(X1, X2, X3)
U131(mark(X1), X2, X3) → U131(X1, X2, X3)
U131(X1, X2, mark(X3)) → U131(X1, X2, X3)
U131(active(X1), X2, X3) → U131(X1, X2, X3)
U131(X1, active(X2), X3) → U131(X1, X2, X3)
U131(X1, X2, active(X3)) → U131(X1, X2, X3)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U131(X1, mark(X2), X3) → U131(X1, X2, X3)
U131(mark(X1), X2, X3) → U131(X1, X2, X3)
U131(X1, X2, mark(X3)) → U131(X1, X2, X3)
U131(active(X1), X2, X3) → U131(X1, X2, X3)
U131(X1, active(X2), X3) → U131(X1, X2, X3)
U131(X1, X2, active(X3)) → U131(X1, X2, X3)
From the DPs we obtained the following set of size-change graphs:
ISNATKIND(active(X)) → ISNATKIND(X)
ISNATKIND(mark(X)) → ISNATKIND(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
ISNATKIND(active(X)) → ISNATKIND(X)
ISNATKIND(mark(X)) → ISNATKIND(X)
From the DPs we obtained the following set of size-change graphs:
U121(X1, mark(X2), X3) → U121(X1, X2, X3)
U121(mark(X1), X2, X3) → U121(X1, X2, X3)
U121(X1, X2, mark(X3)) → U121(X1, X2, X3)
U121(active(X1), X2, X3) → U121(X1, X2, X3)
U121(X1, active(X2), X3) → U121(X1, X2, X3)
U121(X1, X2, active(X3)) → U121(X1, X2, X3)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U121(X1, mark(X2), X3) → U121(X1, X2, X3)
U121(mark(X1), X2, X3) → U121(X1, X2, X3)
U121(X1, X2, mark(X3)) → U121(X1, X2, X3)
U121(active(X1), X2, X3) → U121(X1, X2, X3)
U121(X1, active(X2), X3) → U121(X1, X2, X3)
U121(X1, X2, active(X3)) → U121(X1, X2, X3)
From the DPs we obtained the following set of size-change graphs:
U111(X1, mark(X2), X3) → U111(X1, X2, X3)
U111(mark(X1), X2, X3) → U111(X1, X2, X3)
U111(X1, X2, mark(X3)) → U111(X1, X2, X3)
U111(active(X1), X2, X3) → U111(X1, X2, X3)
U111(X1, active(X2), X3) → U111(X1, X2, X3)
U111(X1, X2, active(X3)) → U111(X1, X2, X3)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
U111(X1, mark(X2), X3) → U111(X1, X2, X3)
U111(mark(X1), X2, X3) → U111(X1, X2, X3)
U111(X1, X2, mark(X3)) → U111(X1, X2, X3)
U111(active(X1), X2, X3) → U111(X1, X2, X3)
U111(X1, active(X2), X3) → U111(X1, X2, X3)
U111(X1, X2, active(X3)) → U111(X1, X2, X3)
From the DPs we obtained the following set of size-change graphs:
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U16(X)) → ACTIVE(U16(mark(X)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
ACTIVE(U51(tt, N)) → MARK(U52(isNatKind(N), N))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U52(tt, N)) → MARK(N)
MARK(U22(X1, X2)) → MARK(X1)
MARK(U23(X)) → ACTIVE(U23(mark(X)))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X)) → ACTIVE(U32(mark(X)))
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
MARK(U41(X)) → ACTIVE(U41(mark(X)))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
MARK(U51(X1, X2)) → ACTIVE(U51(mark(X1), X2))
ACTIVE(isNat(plus(V1, V2))) → MARK(U11(isNatKind(V1), V1, V2))
MARK(U51(X1, X2)) → MARK(X1)
MARK(U52(X1, X2)) → ACTIVE(U52(mark(X1), X2))
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U52(X1, X2)) → MARK(X1)
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U61(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U62(X1, X2, X3)) → MARK(X1)
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
ACTIVE(plus(N, 0)) → MARK(U51(isNat(N), N))
MARK(U63(X1, X2, X3)) → MARK(X1)
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(U64(X1, X2, X3)) → MARK(X1)
MARK(s(X)) → ACTIVE(s(mark(X)))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
MARK(plus(X1, X2)) → MARK(X1)
MARK(plus(X1, X2)) → MARK(X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(plus(N, 0)) → MARK(U51(isNat(N), N))
POL(0) = 1
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = x1
POL(U12(x1, x2, x3)) = x1
POL(U13(x1, x2, x3)) = x1
POL(U14(x1, x2, x3)) = x1
POL(U15(x1, x2)) = x1
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = x1 + x2
POL(U52(x1, x2)) = x1 + x2
POL(U61(x1, x2, x3)) = x1 + x2 + x3
POL(U62(x1, x2, x3)) = x1 + x2 + x3
POL(U63(x1, x2, x3)) = x1 + x2 + x3
POL(U64(x1, x2, x3)) = x1 + x2 + x3
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = x1 + x2
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(mark(X1), X2) → U51(X1, X2)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
active(isNatKind(0)) → mark(tt)
active(isNat(0)) → mark(tt)
active(U23(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U32(tt)) → mark(tt)
active(U16(tt)) → mark(tt)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
mark(0) → active(0)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
s(active(X)) → s(X)
s(mark(X)) → s(X)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
mark(U32(X)) → active(U32(mark(X)))
mark(U16(X)) → active(U16(mark(X)))
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
mark(U41(X)) → active(U41(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
mark(isNat(X)) → active(isNat(X))
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U52(tt, N)) → mark(N)
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U23(X)) → active(U23(mark(X)))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
mark(tt) → active(tt)
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U16(X)) → ACTIVE(U16(mark(X)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
ACTIVE(U51(tt, N)) → MARK(U52(isNatKind(N), N))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U52(tt, N)) → MARK(N)
MARK(U22(X1, X2)) → MARK(X1)
MARK(U23(X)) → ACTIVE(U23(mark(X)))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X)) → ACTIVE(U32(mark(X)))
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
MARK(U41(X)) → ACTIVE(U41(mark(X)))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
MARK(U51(X1, X2)) → ACTIVE(U51(mark(X1), X2))
ACTIVE(isNat(plus(V1, V2))) → MARK(U11(isNatKind(V1), V1, V2))
MARK(U51(X1, X2)) → MARK(X1)
MARK(U52(X1, X2)) → ACTIVE(U52(mark(X1), X2))
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U52(X1, X2)) → MARK(X1)
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U61(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U62(X1, X2, X3)) → MARK(X1)
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U63(X1, X2, X3)) → MARK(X1)
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(U64(X1, X2, X3)) → MARK(X1)
MARK(s(X)) → ACTIVE(s(mark(X)))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
MARK(plus(X1, X2)) → MARK(X1)
MARK(plus(X1, X2)) → MARK(X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U52(tt, N)) → MARK(N)
MARK(U51(X1, X2)) → MARK(X1)
MARK(U52(X1, X2)) → MARK(X1)
POL(0) = 1
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = x1
POL(U12(x1, x2, x3)) = x1
POL(U13(x1, x2, x3)) = x1
POL(U14(x1, x2, x3)) = x1
POL(U15(x1, x2)) = x1
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 1 + x1 + x2
POL(U52(x1, x2)) = 1 + x1 + x2
POL(U61(x1, x2, x3)) = x1 + x2 + x3
POL(U62(x1, x2, x3)) = x1 + x2 + x3
POL(U63(x1, x2, x3)) = x1 + x2 + x3
POL(U64(x1, x2, x3)) = x1 + x2 + x3
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = x1 + x2
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(mark(X1), X2) → U51(X1, X2)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
active(isNatKind(0)) → mark(tt)
active(isNat(0)) → mark(tt)
active(U23(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U32(tt)) → mark(tt)
active(U16(tt)) → mark(tt)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
mark(0) → active(0)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
s(active(X)) → s(X)
s(mark(X)) → s(X)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
mark(U32(X)) → active(U32(mark(X)))
mark(U16(X)) → active(U16(mark(X)))
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
mark(U41(X)) → active(U41(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
mark(isNat(X)) → active(isNat(X))
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U52(tt, N)) → mark(N)
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U23(X)) → active(U23(mark(X)))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
mark(tt) → active(tt)
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U16(X)) → ACTIVE(U16(mark(X)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
ACTIVE(U51(tt, N)) → MARK(U52(isNatKind(N), N))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
MARK(U23(X)) → ACTIVE(U23(mark(X)))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X)) → ACTIVE(U32(mark(X)))
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
MARK(U41(X)) → ACTIVE(U41(mark(X)))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
MARK(U51(X1, X2)) → ACTIVE(U51(mark(X1), X2))
ACTIVE(isNat(plus(V1, V2))) → MARK(U11(isNatKind(V1), V1, V2))
MARK(U52(X1, X2)) → ACTIVE(U52(mark(X1), X2))
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U61(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U62(X1, X2, X3)) → MARK(X1)
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U63(X1, X2, X3)) → MARK(X1)
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(U64(X1, X2, X3)) → MARK(X1)
MARK(s(X)) → ACTIVE(s(mark(X)))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
MARK(plus(X1, X2)) → MARK(X1)
MARK(plus(X1, X2)) → MARK(X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U51(tt, N)) → MARK(U52(isNatKind(N), N))
POL(0) = 1
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = x1
POL(U12(x1, x2, x3)) = x1
POL(U13(x1, x2, x3)) = x1
POL(U14(x1, x2, x3)) = x1
POL(U15(x1, x2)) = x1
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 1 + x2
POL(U52(x1, x2)) = x2
POL(U61(x1, x2, x3)) = x1 + x2 + x3
POL(U62(x1, x2, x3)) = x1 + x2 + x3
POL(U63(x1, x2, x3)) = x1 + x2 + x3
POL(U64(x1, x2, x3)) = x1 + x2 + x3
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = x1 + x2
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(mark(X1), X2) → U51(X1, X2)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
active(isNatKind(0)) → mark(tt)
active(isNat(0)) → mark(tt)
active(U23(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U32(tt)) → mark(tt)
active(U16(tt)) → mark(tt)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
mark(0) → active(0)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
s(active(X)) → s(X)
s(mark(X)) → s(X)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
mark(U32(X)) → active(U32(mark(X)))
mark(U16(X)) → active(U16(mark(X)))
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
mark(U41(X)) → active(U41(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
mark(isNat(X)) → active(isNat(X))
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U52(tt, N)) → mark(N)
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U23(X)) → active(U23(mark(X)))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
mark(tt) → active(tt)
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U16(X)) → ACTIVE(U16(mark(X)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
MARK(U23(X)) → ACTIVE(U23(mark(X)))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
MARK(U32(X)) → ACTIVE(U32(mark(X)))
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
MARK(U41(X)) → ACTIVE(U41(mark(X)))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
MARK(U51(X1, X2)) → ACTIVE(U51(mark(X1), X2))
ACTIVE(isNat(plus(V1, V2))) → MARK(U11(isNatKind(V1), V1, V2))
MARK(U52(X1, X2)) → ACTIVE(U52(mark(X1), X2))
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U61(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U62(X1, X2, X3)) → MARK(X1)
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U63(X1, X2, X3)) → MARK(X1)
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(U64(X1, X2, X3)) → MARK(X1)
MARK(s(X)) → ACTIVE(s(mark(X)))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
MARK(plus(X1, X2)) → MARK(X1)
MARK(plus(X1, X2)) → MARK(X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U16(X)) → ACTIVE(U16(mark(X)))
MARK(U23(X)) → ACTIVE(U23(mark(X)))
MARK(U32(X)) → ACTIVE(U32(mark(X)))
MARK(U41(X)) → ACTIVE(U41(mark(X)))
MARK(U51(X1, X2)) → ACTIVE(U51(mark(X1), X2))
MARK(U52(X1, X2)) → ACTIVE(U52(mark(X1), X2))
MARK(s(X)) → ACTIVE(s(mark(X)))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 1
POL(U11(x1, x2, x3)) = 1
POL(U12(x1, x2, x3)) = 1
POL(U13(x1, x2, x3)) = 1
POL(U14(x1, x2, x3)) = 1
POL(U15(x1, x2)) = 1
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 1
POL(U22(x1, x2)) = 1
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 1
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 1
POL(U62(x1, x2, x3)) = 1
POL(U63(x1, x2, x3)) = 1
POL(U64(x1, x2, x3)) = 1
POL(active(x1)) = 0
POL(isNat(x1)) = 1
POL(isNatKind(x1)) = 1
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 1
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(mark(X1), X2) → U51(X1, X2)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
s(active(X)) → s(X)
s(mark(X)) → s(X)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(plus(V1, V2))) → MARK(U11(isNatKind(V1), V1, V2))
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U61(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U62(X1, X2, X3)) → MARK(X1)
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U63(X1, X2, X3)) → MARK(X1)
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(U64(X1, X2, X3)) → MARK(X1)
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
MARK(plus(X1, X2)) → MARK(X1)
MARK(plus(X1, X2)) → MARK(X2)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U61(X1, X2, X3)) → MARK(X1)
MARK(U62(X1, X2, X3)) → MARK(X1)
MARK(U63(X1, X2, X3)) → MARK(X1)
MARK(U64(X1, X2, X3)) → MARK(X1)
MARK(plus(X1, X2)) → MARK(X1)
MARK(plus(X1, X2)) → MARK(X2)
POL(0) = 1
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = x1
POL(U12(x1, x2, x3)) = x1
POL(U13(x1, x2, x3)) = x1
POL(U14(x1, x2, x3)) = x1
POL(U15(x1, x2)) = x1
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = x1 + x2
POL(U52(x1, x2)) = x2
POL(U61(x1, x2, x3)) = 1 + x1 + x2 + x3
POL(U62(x1, x2, x3)) = 1 + x1 + x2 + x3
POL(U63(x1, x2, x3)) = 1 + x1 + x2 + x3
POL(U64(x1, x2, x3)) = 1 + x1 + x2 + x3
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 1 + x1 + x2
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
active(isNatKind(0)) → mark(tt)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
active(isNat(0)) → mark(tt)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
active(U23(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
active(U32(tt)) → mark(tt)
active(U16(tt)) → mark(tt)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
mark(0) → active(0)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(mark(X1), X2) → U51(X1, X2)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
mark(U32(X)) → active(U32(mark(X)))
mark(U16(X)) → active(U16(mark(X)))
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
mark(U41(X)) → active(U41(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
mark(isNat(X)) → active(isNat(X))
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U52(tt, N)) → mark(N)
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U23(X)) → active(U23(mark(X)))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
mark(tt) → active(tt)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(plus(V1, V2))) → MARK(U11(isNatKind(V1), V1, V2))
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(isNat(plus(V1, V2))) → MARK(U11(isNatKind(V1), V1, V2))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = x1 + x2 + x3
POL(U12(x1, x2, x3)) = x1 + x2 + x3
POL(U13(x1, x2, x3)) = x1 + x2 + x3
POL(U14(x1, x2, x3)) = x1 + x2 + x3
POL(U15(x1, x2)) = x1 + x2
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1 + x2
POL(U22(x1, x2)) = x1 + x2
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = x2
POL(U52(x1, x2)) = x1 + x2
POL(U61(x1, x2, x3)) = 1 + x2 + x3
POL(U62(x1, x2, x3)) = 1 + x2 + x3
POL(U63(x1, x2, x3)) = 1 + x2 + x3
POL(U64(x1, x2, x3)) = 1 + x2 + x3
POL(active(x1)) = x1
POL(isNat(x1)) = x1
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 1 + x1 + x2
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
active(isNatKind(0)) → mark(tt)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
active(isNat(0)) → mark(tt)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
active(U23(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
active(U32(tt)) → mark(tt)
active(U16(tt)) → mark(tt)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
mark(0) → active(0)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(mark(X1), X2) → U51(X1, X2)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
mark(U32(X)) → active(U32(mark(X)))
mark(U16(X)) → active(U16(mark(X)))
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
mark(U41(X)) → active(U41(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
mark(isNat(X)) → active(isNat(X))
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U52(tt, N)) → mark(N)
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U23(X)) → active(U23(mark(X)))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
mark(tt) → active(tt)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
MARK(U11(X1, X2, X3)) → MARK(X1)
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 1 + x1
POL(U12(x1, x2, x3)) = x1
POL(U13(x1, x2, x3)) = x1
POL(U14(x1, x2, x3)) = x1
POL(U15(x1, x2)) = x1
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U11(tt, V1, V2)) → MARK(U12(isNatKind(V1), V1, V2))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 1 + x2 + x3
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(U12(X1, X2, X3)) → MARK(X1)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U12(X1, X2, X3)) → ACTIVE(U12(mark(X1), X2, X3))
MARK(U12(X1, X2, X3)) → MARK(X1)
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 1 + x1 + x2 + x3
POL(U13(x1, x2, x3)) = x1
POL(U14(x1, x2, x3)) = x1
POL(U15(x1, x2)) = x1
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U12(tt, V1, V2)) → MARK(U13(isNatKind(V2), V1, V2))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 1 + x1 + x2
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 1
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U13(X1, X2, X3)) → MARK(X1)
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U13(X1, X2, X3)) → ACTIVE(U13(mark(X1), X2, X3))
MARK(U13(X1, X2, X3)) → MARK(X1)
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 1 + x1 + x3
POL(U14(x1, x2, x3)) = x1
POL(U15(x1, x2)) = x1
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U13(tt, V1, V2)) → MARK(U14(isNatKind(V2), V1, V2))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 1
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U14(X1, X2, X3)) → MARK(X1)
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U14(X1, X2, X3)) → ACTIVE(U14(mark(X1), X2, X3))
MARK(U14(X1, X2, X3)) → MARK(X1)
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 1 + x1 + x2
POL(U15(x1, x2)) = x1
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U14(tt, V1, V2)) → MARK(U15(isNat(V1), V2))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = x1
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 1
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(U15(X1, X2)) → MARK(X1)
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U15(X1, X2)) → ACTIVE(U15(mark(X1), X2))
MARK(U15(X1, X2)) → MARK(X1)
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 1 + x1
POL(U16(x1)) = x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U15(tt, V2)) → MARK(U16(isNat(V2)))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 1
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U16(X)) → MARK(X)
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U16(X)) → MARK(X)
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 1 + x1
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U22(X1, X2)) → MARK(X1)
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U21(X1, X2)) → MARK(X1)
MARK(U22(X1, X2)) → MARK(X1)
POL(0) = 1
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 1 + x1
POL(U12(x1, x2, x3)) = 1
POL(U13(x1, x2, x3)) = 1 + x1
POL(U14(x1, x2, x3)) = 1
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 1 + x1
POL(U22(x1, x2)) = 1 + x1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = x2
POL(U52(x1, x2)) = x2
POL(U61(x1, x2, x3)) = x3
POL(U62(x1, x2, x3)) = x3
POL(U63(x1, x2, x3)) = x3
POL(U64(x1, x2, x3)) = x3
POL(active(x1)) = x1
POL(isNat(x1)) = 1
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = x1
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
active(isNatKind(0)) → mark(tt)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
active(isNat(0)) → mark(tt)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
active(U23(tt)) → mark(tt)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
active(U41(tt)) → mark(tt)
active(U32(tt)) → mark(tt)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
active(U16(tt)) → mark(tt)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
mark(0) → active(0)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(mark(X1), X2) → U51(X1, X2)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
mark(U32(X)) → active(U32(mark(X)))
mark(U16(X)) → active(U16(mark(X)))
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
mark(U41(X)) → active(U41(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
mark(isNat(X)) → active(isNat(X))
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U52(tt, N)) → mark(N)
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U23(X)) → active(U23(mark(X)))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
mark(tt) → active(tt)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U31(tt, V2)) → MARK(U32(isNatKind(V2)))
POL(0) = 1
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = x2 + x3
POL(U12(x1, x2, x3)) = x2 + x3
POL(U13(x1, x2, x3)) = x2
POL(U14(x1, x2, x3)) = x2
POL(U15(x1, x2)) = x1
POL(U16(x1)) = 1
POL(U21(x1, x2)) = x2
POL(U22(x1, x2)) = x2
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1 + x2
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = x2
POL(U52(x1, x2)) = x2
POL(U61(x1, x2, x3)) = x2 + x3
POL(U62(x1, x2, x3)) = x2 + x3
POL(U63(x1, x2, x3)) = x2 + x3
POL(U64(x1, x2, x3)) = x2 + x3
POL(active(x1)) = x1
POL(isNat(x1)) = x1
POL(isNatKind(x1)) = x1
POL(mark(x1)) = x1
POL(plus(x1, x2)) = x1 + x2
POL(s(x1)) = x1
POL(tt) = 1
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
active(isNatKind(0)) → mark(tt)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
active(isNat(0)) → mark(tt)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
active(U23(tt)) → mark(tt)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
active(U41(tt)) → mark(tt)
active(U32(tt)) → mark(tt)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
active(U16(tt)) → mark(tt)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
mark(0) → active(0)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(mark(X1), X2) → U51(X1, X2)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
mark(U32(X)) → active(U32(mark(X)))
mark(U16(X)) → active(U16(mark(X)))
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
mark(U41(X)) → active(U41(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
mark(isNat(X)) → active(isNat(X))
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U52(tt, N)) → mark(N)
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U23(X)) → active(U23(mark(X)))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
mark(tt) → active(tt)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 1
POL(U22(x1, x2)) = 1
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 1
POL(U62(x1, x2, x3)) = 1
POL(U63(x1, x2, x3)) = 1
POL(U64(x1, x2, x3)) = 1
POL(active(x1)) = 0
POL(isNat(x1)) = 1
POL(isNatKind(x1)) = 1
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 1
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
MARK(U32(X)) → MARK(X)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U32(X)) → MARK(X)
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = 1 + x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
s(active(X)) → s(X)
s(mark(X)) → s(X)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(s(X)) → MARK(X)
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(s(X)) → MARK(X)
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = x2
POL(U52(x1, x2)) = x2
POL(U61(x1, x2, x3)) = 1 + x2 + x3
POL(U62(x1, x2, x3)) = 1 + x2 + x3
POL(U63(x1, x2, x3)) = 1 + x2 + x3
POL(U64(x1, x2, x3)) = 1 + x2 + x3
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = x1 + x2
POL(s(x1)) = 1 + x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
active(isNatKind(0)) → mark(tt)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
active(isNat(0)) → mark(tt)
U15(active(X1), X2) → U15(X1, X2)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
active(U23(tt)) → mark(tt)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
active(U41(tt)) → mark(tt)
active(U32(tt)) → mark(tt)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
active(U16(tt)) → mark(tt)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
mark(0) → active(0)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U51(X1, mark(X2)) → U51(X1, X2)
U51(X1, active(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)
U51(mark(X1), X2) → U51(X1, X2)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U32(active(X)) → U32(X)
U32(mark(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
s(active(X)) → s(X)
s(mark(X)) → s(X)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
plus(mark(X1), X2) → plus(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
mark(U32(X)) → active(U32(mark(X)))
mark(U16(X)) → active(U16(mark(X)))
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
mark(U41(X)) → active(U41(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
mark(isNat(X)) → active(isNat(X))
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U52(tt, N)) → mark(N)
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U23(X)) → active(U23(mark(X)))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
mark(tt) → active(tt)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(plus(X1, X2)) → ACTIVE(plus(mark(X1), mark(X2)))
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 1
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(plus(N, s(M))) → MARK(U61(isNat(M), M, N))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 1 + x2
POL(s(x1)) = 1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U61(X1, X2, X3)) → ACTIVE(U61(mark(X1), X2, X3))
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 1 + x3
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = x2
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
MARK(U23(X)) → MARK(X)
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U61(tt, M, N)) → MARK(U62(isNatKind(M), M, N))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 1 + x2
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U62(X1, X2, X3)) → ACTIVE(U62(mark(X1), X2, X3))
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = x3
POL(U12(x1, x2, x3)) = x2
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = x1
POL(U61(x1, x2, x3)) = x1
POL(U62(x1, x2, x3)) = 1 + x2 + x3
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U62(tt, M, N)) → MARK(U63(isNat(N), M, N))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 1 + x1
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 1
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U63(X1, X2, X3)) → ACTIVE(U63(mark(X1), X2, X3))
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 1 + x2
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = x1
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U63(tt, M, N)) → MARK(U64(isNatKind(N), M, N))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = x1 + x3
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 1
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U64(X1, X2, X3)) → ACTIVE(U64(mark(X1), X2, X3))
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = x3
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = x1
POL(U14(x1, x2, x3)) = x2
POL(U15(x1, x2)) = 0
POL(U16(x1)) = x1
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = x1
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = x2 + x3
POL(U62(x1, x2, x3)) = x2
POL(U63(x1, x2, x3)) = x3
POL(U64(x1, x2, x3)) = 1
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
s(active(X)) → s(X)
s(mark(X)) → s(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U64(tt, M, N)) → MARK(s(plus(N, M)))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = x1
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 1
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(isNatKind(plus(V1, V2))) → MARK(U31(isNatKind(V1), V2))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = x1
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = x1
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 1 + x1
POL(s(x1)) = x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U31(X1, X2)) → MARK(X1)
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U31(X1, X2)) → MARK(X1)
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = 1 + x1
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U41(X)) → MARK(X)
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(isNat(s(V1))) → MARK(U21(isNatKind(V1), V1))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = x2
POL(U22(x1, x2)) = x2
POL(U23(x1)) = x1
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = x1
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = 1 + x1
POL(tt) = 0
U21(active(X1), X2) → U21(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U41(X)) → MARK(X)
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 1
POL(U22(x1, x2)) = 0
POL(U23(x1)) = x1
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U41(X)) → MARK(X)
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(U21(tt, V1)) → MARK(U22(isNatKind(V1), V1))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 0
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = x1
POL(U22(x1, x2)) = 0
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 1
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
MARK(isNat(X)) → ACTIVE(isNat(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U41(X)) → MARK(X)
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(isNat(X)) → ACTIVE(isNat(X))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 1
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 1
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U41(X)) → MARK(X)
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVE(isNatKind(s(V1))) → MARK(U41(isNatKind(V1)))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = x2
POL(U23(x1)) = x1
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = x1
POL(mark(x1)) = x1
POL(plus(x1, x2)) = x1
POL(s(x1)) = 1 + x1
POL(tt) = 0
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(X)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U41(X)) → MARK(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(isNatKind(X)) → ACTIVE(isNatKind(X))
POL(0) = 0
POL(ACTIVE(x1)) = x1
POL(MARK(x1)) = 1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 1
POL(U23(x1)) = 0
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = 0
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = 0
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = 0
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
isNatKind(active(X)) → isNatKind(X)
isNatKind(mark(X)) → isNatKind(X)
U22(mark(X1), X2) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
MARK(U23(X)) → MARK(X)
MARK(U41(X)) → MARK(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(U22(X1, X2)) → ACTIVE(U22(mark(X1), X2))
POL(0) = 0
POL(ACTIVE(x1)) = 0
POL(MARK(x1)) = x1
POL(U11(x1, x2, x3)) = 0
POL(U12(x1, x2, x3)) = 0
POL(U13(x1, x2, x3)) = 0
POL(U14(x1, x2, x3)) = 0
POL(U15(x1, x2)) = 0
POL(U16(x1)) = 0
POL(U21(x1, x2)) = 0
POL(U22(x1, x2)) = 1
POL(U23(x1)) = x1
POL(U31(x1, x2)) = 0
POL(U32(x1)) = 0
POL(U41(x1)) = x1
POL(U51(x1, x2)) = 0
POL(U52(x1, x2)) = 0
POL(U61(x1, x2, x3)) = 0
POL(U62(x1, x2, x3)) = 0
POL(U63(x1, x2, x3)) = 0
POL(U64(x1, x2, x3)) = 0
POL(active(x1)) = x1
POL(isNat(x1)) = 0
POL(isNatKind(x1)) = 0
POL(mark(x1)) = x1
POL(plus(x1, x2)) = 0
POL(s(x1)) = 0
POL(tt) = 0
isNat(active(X)) → isNat(X)
isNat(mark(X)) → isNat(X)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
ACTIVE(U22(tt, V1)) → MARK(U23(isNat(V1)))
MARK(U23(X)) → MARK(X)
MARK(U41(X)) → MARK(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
MARK(U41(X)) → MARK(X)
MARK(U23(X)) → MARK(X)
active(U11(tt, V1, V2)) → mark(U12(isNatKind(V1), V1, V2))
active(U12(tt, V1, V2)) → mark(U13(isNatKind(V2), V1, V2))
active(U13(tt, V1, V2)) → mark(U14(isNatKind(V2), V1, V2))
active(U14(tt, V1, V2)) → mark(U15(isNat(V1), V2))
active(U15(tt, V2)) → mark(U16(isNat(V2)))
active(U16(tt)) → mark(tt)
active(U21(tt, V1)) → mark(U22(isNatKind(V1), V1))
active(U22(tt, V1)) → mark(U23(isNat(V1)))
active(U23(tt)) → mark(tt)
active(U31(tt, V2)) → mark(U32(isNatKind(V2)))
active(U32(tt)) → mark(tt)
active(U41(tt)) → mark(tt)
active(U51(tt, N)) → mark(U52(isNatKind(N), N))
active(U52(tt, N)) → mark(N)
active(U61(tt, M, N)) → mark(U62(isNatKind(M), M, N))
active(U62(tt, M, N)) → mark(U63(isNat(N), M, N))
active(U63(tt, M, N)) → mark(U64(isNatKind(N), M, N))
active(U64(tt, M, N)) → mark(s(plus(N, M)))
active(isNat(0)) → mark(tt)
active(isNat(plus(V1, V2))) → mark(U11(isNatKind(V1), V1, V2))
active(isNat(s(V1))) → mark(U21(isNatKind(V1), V1))
active(isNatKind(0)) → mark(tt)
active(isNatKind(plus(V1, V2))) → mark(U31(isNatKind(V1), V2))
active(isNatKind(s(V1))) → mark(U41(isNatKind(V1)))
active(plus(N, 0)) → mark(U51(isNat(N), N))
active(plus(N, s(M))) → mark(U61(isNat(M), M, N))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(isNatKind(X)) → active(isNatKind(X))
mark(U13(X1, X2, X3)) → active(U13(mark(X1), X2, X3))
mark(U14(X1, X2, X3)) → active(U14(mark(X1), X2, X3))
mark(U15(X1, X2)) → active(U15(mark(X1), X2))
mark(isNat(X)) → active(isNat(X))
mark(U16(X)) → active(U16(mark(X)))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U23(X)) → active(U23(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U32(X)) → active(U32(mark(X)))
mark(U41(X)) → active(U41(mark(X)))
mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U61(X1, X2, X3)) → active(U61(mark(X1), X2, X3))
mark(U62(X1, X2, X3)) → active(U62(mark(X1), X2, X3))
mark(U63(X1, X2, X3)) → active(U63(mark(X1), X2, X3))
mark(U64(X1, X2, X3)) → active(U64(mark(X1), X2, X3))
mark(s(X)) → active(s(mark(X)))
mark(plus(X1, X2)) → active(plus(mark(X1), mark(X2)))
mark(0) → active(0)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)
U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)
U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, active(X3)) → U12(X1, X2, X3)
isNatKind(mark(X)) → isNatKind(X)
isNatKind(active(X)) → isNatKind(X)
U13(mark(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, mark(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, mark(X3)) → U13(X1, X2, X3)
U13(active(X1), X2, X3) → U13(X1, X2, X3)
U13(X1, active(X2), X3) → U13(X1, X2, X3)
U13(X1, X2, active(X3)) → U13(X1, X2, X3)
U14(mark(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, mark(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, mark(X3)) → U14(X1, X2, X3)
U14(active(X1), X2, X3) → U14(X1, X2, X3)
U14(X1, active(X2), X3) → U14(X1, X2, X3)
U14(X1, X2, active(X3)) → U14(X1, X2, X3)
U15(mark(X1), X2) → U15(X1, X2)
U15(X1, mark(X2)) → U15(X1, X2)
U15(active(X1), X2) → U15(X1, X2)
U15(X1, active(X2)) → U15(X1, X2)
isNat(mark(X)) → isNat(X)
isNat(active(X)) → isNat(X)
U16(mark(X)) → U16(X)
U16(active(X)) → U16(X)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(X1, X2)
U22(mark(X1), X2) → U22(X1, X2)
U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)
U22(X1, active(X2)) → U22(X1, X2)
U23(mark(X)) → U23(X)
U23(active(X)) → U23(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U32(mark(X)) → U32(X)
U32(active(X)) → U32(X)
U41(mark(X)) → U41(X)
U41(active(X)) → U41(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(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U61(mark(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, mark(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, mark(X3)) → U61(X1, X2, X3)
U61(active(X1), X2, X3) → U61(X1, X2, X3)
U61(X1, active(X2), X3) → U61(X1, X2, X3)
U61(X1, X2, active(X3)) → U61(X1, X2, X3)
U62(mark(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, mark(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, mark(X3)) → U62(X1, X2, X3)
U62(active(X1), X2, X3) → U62(X1, X2, X3)
U62(X1, active(X2), X3) → U62(X1, X2, X3)
U62(X1, X2, active(X3)) → U62(X1, X2, X3)
U63(mark(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, mark(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, mark(X3)) → U63(X1, X2, X3)
U63(active(X1), X2, X3) → U63(X1, X2, X3)
U63(X1, active(X2), X3) → U63(X1, X2, X3)
U63(X1, X2, active(X3)) → U63(X1, X2, X3)
U64(mark(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, mark(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, mark(X3)) → U64(X1, X2, X3)
U64(active(X1), X2, X3) → U64(X1, X2, X3)
U64(X1, active(X2), X3) → U64(X1, X2, X3)
U64(X1, X2, active(X3)) → U64(X1, X2, X3)
s(mark(X)) → s(X)
s(active(X)) → s(X)
plus(mark(X1), X2) → plus(X1, X2)
plus(X1, mark(X2)) → plus(X1, X2)
plus(active(X1), X2) → plus(X1, X2)
plus(X1, active(X2)) → plus(X1, X2)
MARK(U41(X)) → MARK(X)
MARK(U23(X)) → MARK(X)
From the DPs we obtained the following set of size-change graphs: