* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
U105(mark(X1),X2) -> mark(U105(X1,X2))
U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
U106(mark(X)) -> mark(U106(X))
U106(ok(X)) -> ok(U106(X))
U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
U111(mark(X1),X2) -> mark(U111(X1,X2))
U111(ok(X1),ok(X2)) -> ok(U111(X1,X2))
U112(mark(X)) -> mark(U112(X))
U112(ok(X)) -> ok(U112(X))
U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
U121(mark(X1),X2) -> mark(U121(X1,X2))
U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
U122(mark(X)) -> mark(U122(X))
U122(ok(X)) -> ok(U122(X))
U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
U131(mark(X)) -> mark(U131(X))
U131(ok(X)) -> ok(U131(X))
U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
U141(mark(X)) -> mark(U141(X))
U141(ok(X)) -> ok(U141(X))
U151(mark(X)) -> mark(U151(X))
U151(ok(X)) -> ok(U151(X))
U161(mark(X)) -> mark(U161(X))
U161(ok(X)) -> ok(U161(X))
U171(mark(X1),X2) -> mark(U171(X1,X2))
U171(ok(X1),ok(X2)) -> ok(U171(X1,X2))
U172(mark(X)) -> mark(U172(X))
U172(ok(X)) -> ok(U172(X))
U181(mark(X1),X2) -> mark(U181(X1,X2))
U181(ok(X1),ok(X2)) -> ok(U181(X1,X2))
U182(mark(X1),X2) -> mark(U182(X1,X2))
U182(ok(X1),ok(X2)) -> ok(U182(X1,X2))
U183(mark(X)) -> mark(U183(X))
U183(ok(X)) -> ok(U183(X))
U191(mark(X1),X2) -> mark(U191(X1,X2))
U191(ok(X1),ok(X2)) -> ok(U191(X1,X2))
U192(mark(X1),X2) -> mark(U192(X1,X2))
U192(ok(X1),ok(X2)) -> ok(U192(X1,X2))
U193(mark(X)) -> mark(U193(X))
U193(ok(X)) -> ok(U193(X))
U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3))
U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3))
U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3))
U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3))
U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3))
U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3))
U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3))
U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3))
U205(mark(X1),X2) -> mark(U205(X1,X2))
U205(ok(X1),ok(X2)) -> ok(U205(X1,X2))
U206(mark(X)) -> mark(U206(X))
U206(ok(X)) -> ok(U206(X))
U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
U211(mark(X)) -> mark(U211(X))
U211(ok(X)) -> ok(U211(X))
U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
U221(mark(X)) -> mark(U221(X))
U221(ok(X)) -> ok(U221(X))
U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
U231(mark(X1),X2) -> mark(U231(X1,X2))
U231(ok(X1),ok(X2)) -> ok(U231(X1,X2))
U232(mark(X)) -> mark(U232(X))
U232(ok(X)) -> ok(U232(X))
U24(mark(X1),X2) -> mark(U24(X1,X2))
U24(ok(X1),ok(X2)) -> ok(U24(X1,X2))
U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3))
U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3))
U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3))
U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3))
U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3))
U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3))
U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3))
U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3))
U245(mark(X1),X2) -> mark(U245(X1,X2))
U245(ok(X1),ok(X2)) -> ok(U245(X1,X2))
U246(mark(X)) -> mark(U246(X))
U246(ok(X)) -> ok(U246(X))
U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3))
U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3))
U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3))
U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3))
U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3))
U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3))
U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3))
U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3))
U255(mark(X1),X2) -> mark(U255(X1,X2))
U255(ok(X1),ok(X2)) -> ok(U255(X1,X2))
U256(mark(X)) -> mark(U256(X))
U256(ok(X)) -> ok(U256(X))
U261(mark(X1),X2) -> mark(U261(X1,X2))
U261(ok(X1),ok(X2)) -> ok(U261(X1,X2))
U262(mark(X)) -> mark(U262(X))
U262(ok(X)) -> ok(U262(X))
U271(mark(X1),X2) -> mark(U271(X1,X2))
U271(ok(X1),ok(X2)) -> ok(U271(X1,X2))
U272(mark(X)) -> mark(U272(X))
U272(ok(X)) -> ok(U272(X))
U281(mark(X1),X2) -> mark(U281(X1,X2))
U281(ok(X1),ok(X2)) -> ok(U281(X1,X2))
U282(mark(X1),X2) -> mark(U282(X1,X2))
U282(ok(X1),ok(X2)) -> ok(U282(X1,X2))
U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3))
U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3))
U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3))
U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3))
U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3))
U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3))
U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3))
U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3))
U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3))
U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3))
U302(mark(X1),X2) -> mark(U302(X1,X2))
U302(ok(X1),ok(X2)) -> ok(U302(X1,X2))
U303(mark(X1),X2) -> mark(U303(X1,X2))
U303(ok(X1),ok(X2)) -> ok(U303(X1,X2))
U304(mark(X1),X2) -> mark(U304(X1,X2))
U304(ok(X1),ok(X2)) -> ok(U304(X1,X2))
U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3))
U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3))
U311(mark(X1),X2) -> mark(U311(X1,X2))
U311(ok(X1),ok(X2)) -> ok(U311(X1,X2))
U312(mark(X1),X2) -> mark(U312(X1,X2))
U312(ok(X1),ok(X2)) -> ok(U312(X1,X2))
U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3))
U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3))
U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4))
U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4))
U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4))
U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4))
U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4))
U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4))
U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4))
U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4))
U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4))
U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4))
U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4))
U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4))
U327(mark(X1),X2) -> mark(U327(X1,X2))
U327(ok(X1),ok(X2)) -> ok(U327(X1,X2))
U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3))
U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3))
U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3))
U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3))
U332(mark(X1),X2) -> mark(U332(X1,X2))
U332(ok(X1),ok(X2)) -> ok(U332(X1,X2))
U333(mark(X1),X2) -> mark(U333(X1,X2))
U333(ok(X1),ok(X2)) -> ok(U333(X1,X2))
U334(mark(X1),X2) -> mark(U334(X1,X2))
U334(ok(X1),ok(X2)) -> ok(U334(X1,X2))
U34(mark(X1),X2) -> mark(U34(X1,X2))
U34(ok(X1),ok(X2)) -> ok(U34(X1,X2))
U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3))
U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3))
U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3))
U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3))
U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3))
U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3))
U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3))
U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
U45(mark(X1),X2) -> mark(U45(X1,X2))
U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
U46(mark(X)) -> mark(U46(X))
U46(ok(X)) -> ok(U46(X))
U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
U55(mark(X1),X2) -> mark(U55(X1,X2))
U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
U56(mark(X)) -> mark(U56(X))
U56(ok(X)) -> ok(U56(X))
U61(mark(X1),X2) -> mark(U61(X1,X2))
U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
U62(mark(X1),X2) -> mark(U62(X1,X2))
U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
U63(mark(X)) -> mark(U63(X))
U63(ok(X)) -> ok(U63(X))
U71(mark(X1),X2) -> mark(U71(X1,X2))
U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
U72(mark(X1),X2) -> mark(U72(X1,X2))
U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
U73(mark(X)) -> mark(U73(X))
U73(ok(X)) -> ok(U73(X))
U81(mark(X1),X2) -> mark(U81(X1,X2))
U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
U82(mark(X1),X2) -> mark(U82(X1,X2))
U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
U83(mark(X)) -> mark(U83(X))
U83(ok(X)) -> ok(U83(X))
U91(mark(X1),X2) -> mark(U91(X1,X2))
U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
U92(mark(X1),X2) -> mark(U92(X1,X2))
U92(ok(X1),ok(X2)) -> ok(U92(X1,X2))
U93(mark(X)) -> mark(U93(X))
U93(ok(X)) -> ok(U93(X))
active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2))
active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2))
active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2))
active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2))
active(U105(X1,X2)) -> U105(active(X1),X2)
active(U105(tt(),V2)) -> mark(U106(isLNat(V2)))
active(U106(X)) -> U106(active(X))
active(U106(tt())) -> mark(tt())
active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS))
active(U111(X1,X2)) -> U111(active(X1),X2)
active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2)))
active(U112(X)) -> U112(active(X))
active(U112(tt())) -> mark(tt())
active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS))
active(U121(X1,X2)) -> U121(active(X1),X2)
active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2)))
active(U122(X)) -> U122(active(X))
active(U122(tt())) -> mark(tt())
active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS))
active(U131(X)) -> U131(active(X))
active(U131(tt())) -> mark(tt())
active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
active(U141(X)) -> U141(active(X))
active(U141(tt())) -> mark(tt())
active(U151(X)) -> U151(active(X))
active(U151(tt())) -> mark(tt())
active(U161(X)) -> U161(active(X))
active(U161(tt())) -> mark(tt())
active(U171(X1,X2)) -> U171(active(X1),X2)
active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2)))
active(U172(X)) -> U172(active(X))
active(U172(tt())) -> mark(tt())
active(U181(X1,X2)) -> U181(active(X1),X2)
active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1))
active(U182(X1,X2)) -> U182(active(X1),X2)
active(U182(tt(),V1)) -> mark(U183(isLNat(V1)))
active(U183(X)) -> U183(active(X))
active(U183(tt())) -> mark(tt())
active(U191(X1,X2)) -> U191(active(X1),X2)
active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1))
active(U192(X1,X2)) -> U192(active(X1),X2)
active(U192(tt(),V1)) -> mark(U193(isNatural(V1)))
active(U193(X)) -> U193(active(X))
active(U193(tt())) -> mark(tt())
active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3)
active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2))
active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3)
active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2))
active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3)
active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2))
active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3)
active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2))
active(U205(X1,X2)) -> U205(active(X1),X2)
active(U205(tt(),V2)) -> mark(U206(isLNat(V2)))
active(U206(X)) -> U206(active(X))
active(U206(tt())) -> mark(tt())
active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y))
active(U211(X)) -> U211(active(X))
active(U211(tt())) -> mark(tt())
active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y))
active(U221(X)) -> U221(active(X))
active(U221(tt())) -> mark(tt())
active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X))
active(U231(X1,X2)) -> U231(active(X1),X2)
active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2)))
active(U232(X)) -> U232(active(X))
active(U232(tt())) -> mark(tt())
active(U24(X1,X2)) -> U24(active(X1),X2)
active(U24(tt(),X)) -> mark(X)
active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3)
active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2))
active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3)
active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2))
active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3)
active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2))
active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3)
active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2))
active(U245(X1,X2)) -> U245(active(X1),X2)
active(U245(tt(),V2)) -> mark(U246(isLNat(V2)))
active(U246(X)) -> U246(active(X))
active(U246(tt())) -> mark(tt())
active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3)
active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2))
active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3)
active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2))
active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3)
active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2))
active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3)
active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2))
active(U255(X1,X2)) -> U255(active(X1),X2)
active(U255(tt(),V2)) -> mark(U256(isLNat(V2)))
active(U256(X)) -> U256(active(X))
active(U256(tt())) -> mark(tt())
active(U261(X1,X2)) -> U261(active(X1),X2)
active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2)))
active(U262(X)) -> U262(active(X))
active(U262(tt())) -> mark(tt())
active(U271(X1,X2)) -> U271(active(X1),X2)
active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2)))
active(U272(X)) -> U272(active(X))
active(U272(tt())) -> mark(tt())
active(U281(X1,X2)) -> U281(active(X1),X2)
active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N))
active(U282(X1,X2)) -> U282(active(X1),X2)
active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3)
active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS))
active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3)
active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS))
active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3)
active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS))
active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3)
active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3)
active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y))
active(U302(X1,X2)) -> U302(active(X1),X2)
active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y))
active(U303(X1,X2)) -> U303(active(X1),X2)
active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y))
active(U304(X1,X2)) -> U304(active(X1),X2)
active(U304(tt(),Y)) -> mark(Y)
active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3)
active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS))
active(U311(X1,X2)) -> U311(active(X1),X2)
active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS))
active(U312(X1,X2)) -> U312(active(X1),X2)
active(U312(tt(),XS)) -> mark(pair(nil(),XS))
active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3)
active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS))
active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4)
active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS))
active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4)
active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS))
active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4)
active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS))
active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4)
active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS))
active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4)
active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS))
active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4)
active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X))
active(U327(X1,X2)) -> U327(active(X1),X2)
active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3)
active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N))
active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3)
active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS))
active(U332(X1,X2)) -> U332(active(X1),X2)
active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS))
active(U333(X1,X2)) -> U333(active(X1),X2)
active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS))
active(U334(X1,X2)) -> U334(active(X1),X2)
active(U334(tt(),XS)) -> mark(XS)
active(U34(X1,X2)) -> U34(active(X1),X2)
active(U34(tt(),N)) -> mark(N)
active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3)
active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS))
active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3)
active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS))
active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3)
active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS))
active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3)
active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2))
active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2))
active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2))
active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2))
active(U45(X1,X2)) -> U45(active(X1),X2)
active(U45(tt(),V2)) -> mark(U46(isLNat(V2)))
active(U46(X)) -> U46(active(X))
active(U46(tt())) -> mark(tt())
active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2))
active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2))
active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2))
active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2))
active(U55(X1,X2)) -> U55(active(X1),X2)
active(U55(tt(),V2)) -> mark(U56(isLNat(V2)))
active(U56(X)) -> U56(active(X))
active(U56(tt())) -> mark(tt())
active(U61(X1,X2)) -> U61(active(X1),X2)
active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1))
active(U62(X1,X2)) -> U62(active(X1),X2)
active(U62(tt(),V1)) -> mark(U63(isPLNat(V1)))
active(U63(X)) -> U63(active(X))
active(U63(tt())) -> mark(tt())
active(U71(X1,X2)) -> U71(active(X1),X2)
active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1))
active(U72(X1,X2)) -> U72(active(X1),X2)
active(U72(tt(),V1)) -> mark(U73(isNatural(V1)))
active(U73(X)) -> U73(active(X))
active(U73(tt())) -> mark(tt())
active(U81(X1,X2)) -> U81(active(X1),X2)
active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1))
active(U82(X1,X2)) -> U82(active(X1),X2)
active(U82(tt(),V1)) -> mark(U83(isPLNat(V1)))
active(U83(X)) -> U83(active(X))
active(U83(tt())) -> mark(tt())
active(U91(X1,X2)) -> U91(active(X1),X2)
active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1))
active(U92(X1,X2)) -> U92(active(X1),X2)
active(U92(tt(),V1)) -> mark(U93(isLNat(V1)))
active(U93(X)) -> U93(active(X))
active(U93(tt())) -> mark(tt())
active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
active(cons(X1,X2)) -> cons(active(X1),X2)
active(fst(X)) -> fst(active(X))
active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
active(head(X)) -> head(active(X))
active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2))
active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2))
active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
active(isLNat(nil())) -> mark(tt())
active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2))
active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2))
active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2))
active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1)))
active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1)))
active(isLNatKind(nil())) -> mark(tt())
active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1)))
active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1)))
active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2))
active(isNatural(0())) -> mark(tt())
active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1))
active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1))
active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2))
active(isNaturalKind(0())) -> mark(tt())
active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1)))
active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1)))
active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2))
active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2))
active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2))
active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2))
active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2))
active(natsFrom(N)) -> mark(U281(isNatural(N),N))
active(natsFrom(X)) -> natsFrom(active(X))
active(pair(X1,X2)) -> pair(X1,active(X2))
active(pair(X1,X2)) -> pair(active(X1),X2)
active(s(X)) -> s(active(X))
active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS))
active(sel(X1,X2)) -> sel(X1,active(X2))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(snd(X)) -> snd(active(X))
active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y))
active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS))
active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS))
active(tail(X)) -> tail(active(X))
active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS))
active(take(N,XS)) -> mark(U341(isNatural(N),N,XS))
active(take(X1,X2)) -> take(X1,active(X2))
active(take(X1,X2)) -> take(active(X1),X2)
afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
fst(mark(X)) -> mark(fst(X))
fst(ok(X)) -> ok(fst(X))
head(mark(X)) -> mark(head(X))
head(ok(X)) -> ok(head(X))
isLNat(ok(X)) -> ok(isLNat(X))
isLNatKind(ok(X)) -> ok(isLNatKind(X))
isNatural(ok(X)) -> ok(isNatural(X))
isNaturalKind(ok(X)) -> ok(isNaturalKind(X))
isPLNat(ok(X)) -> ok(isPLNat(X))
isPLNatKind(ok(X)) -> ok(isPLNatKind(X))
natsFrom(mark(X)) -> mark(natsFrom(X))
natsFrom(ok(X)) -> ok(natsFrom(X))
pair(X1,mark(X2)) -> mark(pair(X1,X2))
pair(mark(X1),X2) -> mark(pair(X1,X2))
pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
proper(0()) -> ok(0())
proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
proper(U106(X)) -> U106(proper(X))
proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
proper(U111(X1,X2)) -> U111(proper(X1),proper(X2))
proper(U112(X)) -> U112(proper(X))
proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
proper(U122(X)) -> U122(proper(X))
proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
proper(U131(X)) -> U131(proper(X))
proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
proper(U141(X)) -> U141(proper(X))
proper(U151(X)) -> U151(proper(X))
proper(U161(X)) -> U161(proper(X))
proper(U171(X1,X2)) -> U171(proper(X1),proper(X2))
proper(U172(X)) -> U172(proper(X))
proper(U181(X1,X2)) -> U181(proper(X1),proper(X2))
proper(U182(X1,X2)) -> U182(proper(X1),proper(X2))
proper(U183(X)) -> U183(proper(X))
proper(U191(X1,X2)) -> U191(proper(X1),proper(X2))
proper(U192(X1,X2)) -> U192(proper(X1),proper(X2))
proper(U193(X)) -> U193(proper(X))
proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3))
proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3))
proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3))
proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3))
proper(U205(X1,X2)) -> U205(proper(X1),proper(X2))
proper(U206(X)) -> U206(proper(X))
proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
proper(U211(X)) -> U211(proper(X))
proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
proper(U221(X)) -> U221(proper(X))
proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
proper(U231(X1,X2)) -> U231(proper(X1),proper(X2))
proper(U232(X)) -> U232(proper(X))
proper(U24(X1,X2)) -> U24(proper(X1),proper(X2))
proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3))
proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3))
proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3))
proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3))
proper(U245(X1,X2)) -> U245(proper(X1),proper(X2))
proper(U246(X)) -> U246(proper(X))
proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3))
proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3))
proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3))
proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3))
proper(U255(X1,X2)) -> U255(proper(X1),proper(X2))
proper(U256(X)) -> U256(proper(X))
proper(U261(X1,X2)) -> U261(proper(X1),proper(X2))
proper(U262(X)) -> U262(proper(X))
proper(U271(X1,X2)) -> U271(proper(X1),proper(X2))
proper(U272(X)) -> U272(proper(X))
proper(U281(X1,X2)) -> U281(proper(X1),proper(X2))
proper(U282(X1,X2)) -> U282(proper(X1),proper(X2))
proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3))
proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3))
proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3))
proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3))
proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3))
proper(U302(X1,X2)) -> U302(proper(X1),proper(X2))
proper(U303(X1,X2)) -> U303(proper(X1),proper(X2))
proper(U304(X1,X2)) -> U304(proper(X1),proper(X2))
proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3))
proper(U311(X1,X2)) -> U311(proper(X1),proper(X2))
proper(U312(X1,X2)) -> U312(proper(X1),proper(X2))
proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3))
proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U327(X1,X2)) -> U327(proper(X1),proper(X2))
proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3))
proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3))
proper(U332(X1,X2)) -> U332(proper(X1),proper(X2))
proper(U333(X1,X2)) -> U333(proper(X1),proper(X2))
proper(U334(X1,X2)) -> U334(proper(X1),proper(X2))
proper(U34(X1,X2)) -> U34(proper(X1),proper(X2))
proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3))
proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3))
proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3))
proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3))
proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
proper(U46(X)) -> U46(proper(X))
proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
proper(U56(X)) -> U56(proper(X))
proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
proper(U63(X)) -> U63(proper(X))
proper(U71(X1,X2)) -> U71(proper(X1),proper(X2))
proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
proper(U73(X)) -> U73(proper(X))
proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
proper(U83(X)) -> U83(proper(X))
proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
proper(U92(X1,X2)) -> U92(proper(X1),proper(X2))
proper(U93(X)) -> U93(proper(X))
proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(fst(X)) -> fst(proper(X))
proper(head(X)) -> head(proper(X))
proper(isLNat(X)) -> isLNat(proper(X))
proper(isLNatKind(X)) -> isLNatKind(proper(X))
proper(isNatural(X)) -> isNatural(proper(X))
proper(isNaturalKind(X)) -> isNaturalKind(proper(X))
proper(isPLNat(X)) -> isPLNat(proper(X))
proper(isPLNatKind(X)) -> isPLNatKind(proper(X))
proper(natsFrom(X)) -> natsFrom(proper(X))
proper(nil()) -> ok(nil())
proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(snd(X)) -> snd(proper(X))
proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
proper(tail(X)) -> tail(proper(X))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(tt()) -> ok(tt())
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
snd(mark(X)) -> mark(snd(X))
snd(ok(X)) -> ok(snd(X))
splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
tail(mark(X)) -> mark(tail(X))
tail(ok(X)) -> ok(tail(X))
take(X1,mark(X2)) -> mark(take(X1,X2))
take(mark(X1),X2) -> mark(take(X1,X2))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{U101/3,U102/3,U103/3,U104/3,U105/2,U106/1,U11/3,U111/2,U112/1,U12/3,U121/2,U122/1,U13/3,U131/1,U14/3,U141/1
,U151/1,U161/1,U171/2,U172/1,U181/2,U182/2,U183/1,U191/2,U192/2,U193/1,U201/3,U202/3,U203/3,U204/3,U205/2
,U206/1,U21/3,U211/1,U22/3,U221/1,U23/3,U231/2,U232/1,U24/2,U241/3,U242/3,U243/3,U244/3,U245/2,U246/1,U251/3
,U252/3,U253/3,U254/3,U255/2,U256/1,U261/2,U262/1,U271/2,U272/1,U281/2,U282/2,U291/3,U292/3,U293/3,U294/3
,U301/3,U302/2,U303/2,U304/2,U31/3,U311/2,U312/2,U32/3,U321/4,U322/4,U323/4,U324/4,U325/4,U326/4,U327/2
,U33/3,U331/3,U332/2,U333/2,U334/2,U34/2,U341/3,U342/3,U343/3,U344/3,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1
,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/2,U72/2,U73/1,U81/2,U82/2,U83/1,U91/2,U92/2,U93/1
,active/1,afterNth/2,cons/2,fst/1,head/1,isLNat/1,isLNatKind/1,isNatural/1,isNaturalKind/1,isPLNat/1
,isPLNatKind/1,natsFrom/1,pair/2,proper/1,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2,top/1} / {0/0,mark/1,nil/0
,ok/1,tt/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {U101,U102,U103,U104,U105,U106,U11,U111,U112,U12,U121,U122
,U13,U131,U14,U141,U151,U161,U171,U172,U181,U182,U183,U191,U192,U193,U201,U202,U203,U204,U205,U206,U21,U211
,U22,U221,U23,U231,U232,U24,U241,U242,U243,U244,U245,U246,U251,U252,U253,U254,U255,U256,U261,U262,U271,U272
,U281,U282,U291,U292,U293,U294,U301,U302,U303,U304,U31,U311,U312,U32,U321,U322,U323,U324,U325,U326,U327,U33
,U331,U332,U333,U334,U34,U341,U342,U343,U344,U41,U42,U43,U44,U45,U46,U51,U52,U53,U54,U55,U56,U61,U62,U63,U71
,U72,U73,U81,U82,U83,U91,U92,U93,active,afterNth,cons,fst,head,isLNat,isLNatKind,isNatural,isNaturalKind
,isPLNat,isPLNatKind,natsFrom,pair,proper,s,sel,snd,splitAt,tail,take,top} and constructors {0,mark,nil,ok
,tt}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
U105(mark(X1),X2) -> mark(U105(X1,X2))
U105(ok(X1),ok(X2)) -> ok(U105(X1,X2))
U106(mark(X)) -> mark(U106(X))
U106(ok(X)) -> ok(U106(X))
U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
U111(mark(X1),X2) -> mark(U111(X1,X2))
U111(ok(X1),ok(X2)) -> ok(U111(X1,X2))
U112(mark(X)) -> mark(U112(X))
U112(ok(X)) -> ok(U112(X))
U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
U121(mark(X1),X2) -> mark(U121(X1,X2))
U121(ok(X1),ok(X2)) -> ok(U121(X1,X2))
U122(mark(X)) -> mark(U122(X))
U122(ok(X)) -> ok(U122(X))
U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
U131(mark(X)) -> mark(U131(X))
U131(ok(X)) -> ok(U131(X))
U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
U141(mark(X)) -> mark(U141(X))
U141(ok(X)) -> ok(U141(X))
U151(mark(X)) -> mark(U151(X))
U151(ok(X)) -> ok(U151(X))
U161(mark(X)) -> mark(U161(X))
U161(ok(X)) -> ok(U161(X))
U171(mark(X1),X2) -> mark(U171(X1,X2))
U171(ok(X1),ok(X2)) -> ok(U171(X1,X2))
U172(mark(X)) -> mark(U172(X))
U172(ok(X)) -> ok(U172(X))
U181(mark(X1),X2) -> mark(U181(X1,X2))
U181(ok(X1),ok(X2)) -> ok(U181(X1,X2))
U182(mark(X1),X2) -> mark(U182(X1,X2))
U182(ok(X1),ok(X2)) -> ok(U182(X1,X2))
U183(mark(X)) -> mark(U183(X))
U183(ok(X)) -> ok(U183(X))
U191(mark(X1),X2) -> mark(U191(X1,X2))
U191(ok(X1),ok(X2)) -> ok(U191(X1,X2))
U192(mark(X1),X2) -> mark(U192(X1,X2))
U192(ok(X1),ok(X2)) -> ok(U192(X1,X2))
U193(mark(X)) -> mark(U193(X))
U193(ok(X)) -> ok(U193(X))
U201(mark(X1),X2,X3) -> mark(U201(X1,X2,X3))
U201(ok(X1),ok(X2),ok(X3)) -> ok(U201(X1,X2,X3))
U202(mark(X1),X2,X3) -> mark(U202(X1,X2,X3))
U202(ok(X1),ok(X2),ok(X3)) -> ok(U202(X1,X2,X3))
U203(mark(X1),X2,X3) -> mark(U203(X1,X2,X3))
U203(ok(X1),ok(X2),ok(X3)) -> ok(U203(X1,X2,X3))
U204(mark(X1),X2,X3) -> mark(U204(X1,X2,X3))
U204(ok(X1),ok(X2),ok(X3)) -> ok(U204(X1,X2,X3))
U205(mark(X1),X2) -> mark(U205(X1,X2))
U205(ok(X1),ok(X2)) -> ok(U205(X1,X2))
U206(mark(X)) -> mark(U206(X))
U206(ok(X)) -> ok(U206(X))
U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
U211(mark(X)) -> mark(U211(X))
U211(ok(X)) -> ok(U211(X))
U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
U221(mark(X)) -> mark(U221(X))
U221(ok(X)) -> ok(U221(X))
U23(mark(X1),X2,X3) -> mark(U23(X1,X2,X3))
U23(ok(X1),ok(X2),ok(X3)) -> ok(U23(X1,X2,X3))
U231(mark(X1),X2) -> mark(U231(X1,X2))
U231(ok(X1),ok(X2)) -> ok(U231(X1,X2))
U232(mark(X)) -> mark(U232(X))
U232(ok(X)) -> ok(U232(X))
U24(mark(X1),X2) -> mark(U24(X1,X2))
U24(ok(X1),ok(X2)) -> ok(U24(X1,X2))
U241(mark(X1),X2,X3) -> mark(U241(X1,X2,X3))
U241(ok(X1),ok(X2),ok(X3)) -> ok(U241(X1,X2,X3))
U242(mark(X1),X2,X3) -> mark(U242(X1,X2,X3))
U242(ok(X1),ok(X2),ok(X3)) -> ok(U242(X1,X2,X3))
U243(mark(X1),X2,X3) -> mark(U243(X1,X2,X3))
U243(ok(X1),ok(X2),ok(X3)) -> ok(U243(X1,X2,X3))
U244(mark(X1),X2,X3) -> mark(U244(X1,X2,X3))
U244(ok(X1),ok(X2),ok(X3)) -> ok(U244(X1,X2,X3))
U245(mark(X1),X2) -> mark(U245(X1,X2))
U245(ok(X1),ok(X2)) -> ok(U245(X1,X2))
U246(mark(X)) -> mark(U246(X))
U246(ok(X)) -> ok(U246(X))
U251(mark(X1),X2,X3) -> mark(U251(X1,X2,X3))
U251(ok(X1),ok(X2),ok(X3)) -> ok(U251(X1,X2,X3))
U252(mark(X1),X2,X3) -> mark(U252(X1,X2,X3))
U252(ok(X1),ok(X2),ok(X3)) -> ok(U252(X1,X2,X3))
U253(mark(X1),X2,X3) -> mark(U253(X1,X2,X3))
U253(ok(X1),ok(X2),ok(X3)) -> ok(U253(X1,X2,X3))
U254(mark(X1),X2,X3) -> mark(U254(X1,X2,X3))
U254(ok(X1),ok(X2),ok(X3)) -> ok(U254(X1,X2,X3))
U255(mark(X1),X2) -> mark(U255(X1,X2))
U255(ok(X1),ok(X2)) -> ok(U255(X1,X2))
U256(mark(X)) -> mark(U256(X))
U256(ok(X)) -> ok(U256(X))
U261(mark(X1),X2) -> mark(U261(X1,X2))
U261(ok(X1),ok(X2)) -> ok(U261(X1,X2))
U262(mark(X)) -> mark(U262(X))
U262(ok(X)) -> ok(U262(X))
U271(mark(X1),X2) -> mark(U271(X1,X2))
U271(ok(X1),ok(X2)) -> ok(U271(X1,X2))
U272(mark(X)) -> mark(U272(X))
U272(ok(X)) -> ok(U272(X))
U281(mark(X1),X2) -> mark(U281(X1,X2))
U281(ok(X1),ok(X2)) -> ok(U281(X1,X2))
U282(mark(X1),X2) -> mark(U282(X1,X2))
U282(ok(X1),ok(X2)) -> ok(U282(X1,X2))
U291(mark(X1),X2,X3) -> mark(U291(X1,X2,X3))
U291(ok(X1),ok(X2),ok(X3)) -> ok(U291(X1,X2,X3))
U292(mark(X1),X2,X3) -> mark(U292(X1,X2,X3))
U292(ok(X1),ok(X2),ok(X3)) -> ok(U292(X1,X2,X3))
U293(mark(X1),X2,X3) -> mark(U293(X1,X2,X3))
U293(ok(X1),ok(X2),ok(X3)) -> ok(U293(X1,X2,X3))
U294(mark(X1),X2,X3) -> mark(U294(X1,X2,X3))
U294(ok(X1),ok(X2),ok(X3)) -> ok(U294(X1,X2,X3))
U301(mark(X1),X2,X3) -> mark(U301(X1,X2,X3))
U301(ok(X1),ok(X2),ok(X3)) -> ok(U301(X1,X2,X3))
U302(mark(X1),X2) -> mark(U302(X1,X2))
U302(ok(X1),ok(X2)) -> ok(U302(X1,X2))
U303(mark(X1),X2) -> mark(U303(X1,X2))
U303(ok(X1),ok(X2)) -> ok(U303(X1,X2))
U304(mark(X1),X2) -> mark(U304(X1,X2))
U304(ok(X1),ok(X2)) -> ok(U304(X1,X2))
U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3))
U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3))
U311(mark(X1),X2) -> mark(U311(X1,X2))
U311(ok(X1),ok(X2)) -> ok(U311(X1,X2))
U312(mark(X1),X2) -> mark(U312(X1,X2))
U312(ok(X1),ok(X2)) -> ok(U312(X1,X2))
U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3))
U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3))
U321(mark(X1),X2,X3,X4) -> mark(U321(X1,X2,X3,X4))
U321(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U321(X1,X2,X3,X4))
U322(mark(X1),X2,X3,X4) -> mark(U322(X1,X2,X3,X4))
U322(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U322(X1,X2,X3,X4))
U323(mark(X1),X2,X3,X4) -> mark(U323(X1,X2,X3,X4))
U323(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U323(X1,X2,X3,X4))
U324(mark(X1),X2,X3,X4) -> mark(U324(X1,X2,X3,X4))
U324(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U324(X1,X2,X3,X4))
U325(mark(X1),X2,X3,X4) -> mark(U325(X1,X2,X3,X4))
U325(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U325(X1,X2,X3,X4))
U326(mark(X1),X2,X3,X4) -> mark(U326(X1,X2,X3,X4))
U326(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U326(X1,X2,X3,X4))
U327(mark(X1),X2) -> mark(U327(X1,X2))
U327(ok(X1),ok(X2)) -> ok(U327(X1,X2))
U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3))
U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3))
U331(mark(X1),X2,X3) -> mark(U331(X1,X2,X3))
U331(ok(X1),ok(X2),ok(X3)) -> ok(U331(X1,X2,X3))
U332(mark(X1),X2) -> mark(U332(X1,X2))
U332(ok(X1),ok(X2)) -> ok(U332(X1,X2))
U333(mark(X1),X2) -> mark(U333(X1,X2))
U333(ok(X1),ok(X2)) -> ok(U333(X1,X2))
U334(mark(X1),X2) -> mark(U334(X1,X2))
U334(ok(X1),ok(X2)) -> ok(U334(X1,X2))
U34(mark(X1),X2) -> mark(U34(X1,X2))
U34(ok(X1),ok(X2)) -> ok(U34(X1,X2))
U341(mark(X1),X2,X3) -> mark(U341(X1,X2,X3))
U341(ok(X1),ok(X2),ok(X3)) -> ok(U341(X1,X2,X3))
U342(mark(X1),X2,X3) -> mark(U342(X1,X2,X3))
U342(ok(X1),ok(X2),ok(X3)) -> ok(U342(X1,X2,X3))
U343(mark(X1),X2,X3) -> mark(U343(X1,X2,X3))
U343(ok(X1),ok(X2),ok(X3)) -> ok(U343(X1,X2,X3))
U344(mark(X1),X2,X3) -> mark(U344(X1,X2,X3))
U344(ok(X1),ok(X2),ok(X3)) -> ok(U344(X1,X2,X3))
U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3))
U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3))
U43(mark(X1),X2,X3) -> mark(U43(X1,X2,X3))
U43(ok(X1),ok(X2),ok(X3)) -> ok(U43(X1,X2,X3))
U44(mark(X1),X2,X3) -> mark(U44(X1,X2,X3))
U44(ok(X1),ok(X2),ok(X3)) -> ok(U44(X1,X2,X3))
U45(mark(X1),X2) -> mark(U45(X1,X2))
U45(ok(X1),ok(X2)) -> ok(U45(X1,X2))
U46(mark(X)) -> mark(U46(X))
U46(ok(X)) -> ok(U46(X))
U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
U53(mark(X1),X2,X3) -> mark(U53(X1,X2,X3))
U53(ok(X1),ok(X2),ok(X3)) -> ok(U53(X1,X2,X3))
U54(mark(X1),X2,X3) -> mark(U54(X1,X2,X3))
U54(ok(X1),ok(X2),ok(X3)) -> ok(U54(X1,X2,X3))
U55(mark(X1),X2) -> mark(U55(X1,X2))
U55(ok(X1),ok(X2)) -> ok(U55(X1,X2))
U56(mark(X)) -> mark(U56(X))
U56(ok(X)) -> ok(U56(X))
U61(mark(X1),X2) -> mark(U61(X1,X2))
U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
U62(mark(X1),X2) -> mark(U62(X1,X2))
U62(ok(X1),ok(X2)) -> ok(U62(X1,X2))
U63(mark(X)) -> mark(U63(X))
U63(ok(X)) -> ok(U63(X))
U71(mark(X1),X2) -> mark(U71(X1,X2))
U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
U72(mark(X1),X2) -> mark(U72(X1,X2))
U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
U73(mark(X)) -> mark(U73(X))
U73(ok(X)) -> ok(U73(X))
U81(mark(X1),X2) -> mark(U81(X1,X2))
U81(ok(X1),ok(X2)) -> ok(U81(X1,X2))
U82(mark(X1),X2) -> mark(U82(X1,X2))
U82(ok(X1),ok(X2)) -> ok(U82(X1,X2))
U83(mark(X)) -> mark(U83(X))
U83(ok(X)) -> ok(U83(X))
U91(mark(X1),X2) -> mark(U91(X1,X2))
U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
U92(mark(X1),X2) -> mark(U92(X1,X2))
U92(ok(X1),ok(X2)) -> ok(U92(X1,X2))
U93(mark(X)) -> mark(U93(X))
U93(ok(X)) -> ok(U93(X))
active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
active(U101(tt(),V1,V2)) -> mark(U102(isNaturalKind(V1),V1,V2))
active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
active(U102(tt(),V1,V2)) -> mark(U103(isLNatKind(V2),V1,V2))
active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
active(U103(tt(),V1,V2)) -> mark(U104(isLNatKind(V2),V1,V2))
active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
active(U104(tt(),V1,V2)) -> mark(U105(isNatural(V1),V2))
active(U105(X1,X2)) -> U105(active(X1),X2)
active(U105(tt(),V2)) -> mark(U106(isLNat(V2)))
active(U106(X)) -> U106(active(X))
active(U106(tt())) -> mark(tt())
active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
active(U11(tt(),N,XS)) -> mark(U12(isNaturalKind(N),N,XS))
active(U111(X1,X2)) -> U111(active(X1),X2)
active(U111(tt(),V2)) -> mark(U112(isLNatKind(V2)))
active(U112(X)) -> U112(active(X))
active(U112(tt())) -> mark(tt())
active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
active(U12(tt(),N,XS)) -> mark(U13(isLNat(XS),N,XS))
active(U121(X1,X2)) -> U121(active(X1),X2)
active(U121(tt(),V2)) -> mark(U122(isLNatKind(V2)))
active(U122(X)) -> U122(active(X))
active(U122(tt())) -> mark(tt())
active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
active(U13(tt(),N,XS)) -> mark(U14(isLNatKind(XS),N,XS))
active(U131(X)) -> U131(active(X))
active(U131(tt())) -> mark(tt())
active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
active(U14(tt(),N,XS)) -> mark(snd(splitAt(N,XS)))
active(U141(X)) -> U141(active(X))
active(U141(tt())) -> mark(tt())
active(U151(X)) -> U151(active(X))
active(U151(tt())) -> mark(tt())
active(U161(X)) -> U161(active(X))
active(U161(tt())) -> mark(tt())
active(U171(X1,X2)) -> U171(active(X1),X2)
active(U171(tt(),V2)) -> mark(U172(isLNatKind(V2)))
active(U172(X)) -> U172(active(X))
active(U172(tt())) -> mark(tt())
active(U181(X1,X2)) -> U181(active(X1),X2)
active(U181(tt(),V1)) -> mark(U182(isLNatKind(V1),V1))
active(U182(X1,X2)) -> U182(active(X1),X2)
active(U182(tt(),V1)) -> mark(U183(isLNat(V1)))
active(U183(X)) -> U183(active(X))
active(U183(tt())) -> mark(tt())
active(U191(X1,X2)) -> U191(active(X1),X2)
active(U191(tt(),V1)) -> mark(U192(isNaturalKind(V1),V1))
active(U192(X1,X2)) -> U192(active(X1),X2)
active(U192(tt(),V1)) -> mark(U193(isNatural(V1)))
active(U193(X)) -> U193(active(X))
active(U193(tt())) -> mark(tt())
active(U201(X1,X2,X3)) -> U201(active(X1),X2,X3)
active(U201(tt(),V1,V2)) -> mark(U202(isNaturalKind(V1),V1,V2))
active(U202(X1,X2,X3)) -> U202(active(X1),X2,X3)
active(U202(tt(),V1,V2)) -> mark(U203(isLNatKind(V2),V1,V2))
active(U203(X1,X2,X3)) -> U203(active(X1),X2,X3)
active(U203(tt(),V1,V2)) -> mark(U204(isLNatKind(V2),V1,V2))
active(U204(X1,X2,X3)) -> U204(active(X1),X2,X3)
active(U204(tt(),V1,V2)) -> mark(U205(isNatural(V1),V2))
active(U205(X1,X2)) -> U205(active(X1),X2)
active(U205(tt(),V2)) -> mark(U206(isLNat(V2)))
active(U206(X)) -> U206(active(X))
active(U206(tt())) -> mark(tt())
active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
active(U21(tt(),X,Y)) -> mark(U22(isLNatKind(X),X,Y))
active(U211(X)) -> U211(active(X))
active(U211(tt())) -> mark(tt())
active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
active(U22(tt(),X,Y)) -> mark(U23(isLNat(Y),X,Y))
active(U221(X)) -> U221(active(X))
active(U221(tt())) -> mark(tt())
active(U23(X1,X2,X3)) -> U23(active(X1),X2,X3)
active(U23(tt(),X,Y)) -> mark(U24(isLNatKind(Y),X))
active(U231(X1,X2)) -> U231(active(X1),X2)
active(U231(tt(),V2)) -> mark(U232(isLNatKind(V2)))
active(U232(X)) -> U232(active(X))
active(U232(tt())) -> mark(tt())
active(U24(X1,X2)) -> U24(active(X1),X2)
active(U24(tt(),X)) -> mark(X)
active(U241(X1,X2,X3)) -> U241(active(X1),X2,X3)
active(U241(tt(),V1,V2)) -> mark(U242(isLNatKind(V1),V1,V2))
active(U242(X1,X2,X3)) -> U242(active(X1),X2,X3)
active(U242(tt(),V1,V2)) -> mark(U243(isLNatKind(V2),V1,V2))
active(U243(X1,X2,X3)) -> U243(active(X1),X2,X3)
active(U243(tt(),V1,V2)) -> mark(U244(isLNatKind(V2),V1,V2))
active(U244(X1,X2,X3)) -> U244(active(X1),X2,X3)
active(U244(tt(),V1,V2)) -> mark(U245(isLNat(V1),V2))
active(U245(X1,X2)) -> U245(active(X1),X2)
active(U245(tt(),V2)) -> mark(U246(isLNat(V2)))
active(U246(X)) -> U246(active(X))
active(U246(tt())) -> mark(tt())
active(U251(X1,X2,X3)) -> U251(active(X1),X2,X3)
active(U251(tt(),V1,V2)) -> mark(U252(isNaturalKind(V1),V1,V2))
active(U252(X1,X2,X3)) -> U252(active(X1),X2,X3)
active(U252(tt(),V1,V2)) -> mark(U253(isLNatKind(V2),V1,V2))
active(U253(X1,X2,X3)) -> U253(active(X1),X2,X3)
active(U253(tt(),V1,V2)) -> mark(U254(isLNatKind(V2),V1,V2))
active(U254(X1,X2,X3)) -> U254(active(X1),X2,X3)
active(U254(tt(),V1,V2)) -> mark(U255(isNatural(V1),V2))
active(U255(X1,X2)) -> U255(active(X1),X2)
active(U255(tt(),V2)) -> mark(U256(isLNat(V2)))
active(U256(X)) -> U256(active(X))
active(U256(tt())) -> mark(tt())
active(U261(X1,X2)) -> U261(active(X1),X2)
active(U261(tt(),V2)) -> mark(U262(isLNatKind(V2)))
active(U262(X)) -> U262(active(X))
active(U262(tt())) -> mark(tt())
active(U271(X1,X2)) -> U271(active(X1),X2)
active(U271(tt(),V2)) -> mark(U272(isLNatKind(V2)))
active(U272(X)) -> U272(active(X))
active(U272(tt())) -> mark(tt())
active(U281(X1,X2)) -> U281(active(X1),X2)
active(U281(tt(),N)) -> mark(U282(isNaturalKind(N),N))
active(U282(X1,X2)) -> U282(active(X1),X2)
active(U282(tt(),N)) -> mark(cons(N,natsFrom(s(N))))
active(U291(X1,X2,X3)) -> U291(active(X1),X2,X3)
active(U291(tt(),N,XS)) -> mark(U292(isNaturalKind(N),N,XS))
active(U292(X1,X2,X3)) -> U292(active(X1),X2,X3)
active(U292(tt(),N,XS)) -> mark(U293(isLNat(XS),N,XS))
active(U293(X1,X2,X3)) -> U293(active(X1),X2,X3)
active(U293(tt(),N,XS)) -> mark(U294(isLNatKind(XS),N,XS))
active(U294(X1,X2,X3)) -> U294(active(X1),X2,X3)
active(U294(tt(),N,XS)) -> mark(head(afterNth(N,XS)))
active(U301(X1,X2,X3)) -> U301(active(X1),X2,X3)
active(U301(tt(),X,Y)) -> mark(U302(isLNatKind(X),Y))
active(U302(X1,X2)) -> U302(active(X1),X2)
active(U302(tt(),Y)) -> mark(U303(isLNat(Y),Y))
active(U303(X1,X2)) -> U303(active(X1),X2)
active(U303(tt(),Y)) -> mark(U304(isLNatKind(Y),Y))
active(U304(X1,X2)) -> U304(active(X1),X2)
active(U304(tt(),Y)) -> mark(Y)
active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3)
active(U31(tt(),N,XS)) -> mark(U32(isNaturalKind(N),N,XS))
active(U311(X1,X2)) -> U311(active(X1),X2)
active(U311(tt(),XS)) -> mark(U312(isLNatKind(XS),XS))
active(U312(X1,X2)) -> U312(active(X1),X2)
active(U312(tt(),XS)) -> mark(pair(nil(),XS))
active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3)
active(U32(tt(),N,XS)) -> mark(U33(isLNat(XS),N,XS))
active(U321(X1,X2,X3,X4)) -> U321(active(X1),X2,X3,X4)
active(U321(tt(),N,X,XS)) -> mark(U322(isNaturalKind(N),N,X,XS))
active(U322(X1,X2,X3,X4)) -> U322(active(X1),X2,X3,X4)
active(U322(tt(),N,X,XS)) -> mark(U323(isNatural(X),N,X,XS))
active(U323(X1,X2,X3,X4)) -> U323(active(X1),X2,X3,X4)
active(U323(tt(),N,X,XS)) -> mark(U324(isNaturalKind(X),N,X,XS))
active(U324(X1,X2,X3,X4)) -> U324(active(X1),X2,X3,X4)
active(U324(tt(),N,X,XS)) -> mark(U325(isLNat(XS),N,X,XS))
active(U325(X1,X2,X3,X4)) -> U325(active(X1),X2,X3,X4)
active(U325(tt(),N,X,XS)) -> mark(U326(isLNatKind(XS),N,X,XS))
active(U326(X1,X2,X3,X4)) -> U326(active(X1),X2,X3,X4)
active(U326(tt(),N,X,XS)) -> mark(U327(splitAt(N,XS),X))
active(U327(X1,X2)) -> U327(active(X1),X2)
active(U327(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3)
active(U33(tt(),N,XS)) -> mark(U34(isLNatKind(XS),N))
active(U331(X1,X2,X3)) -> U331(active(X1),X2,X3)
active(U331(tt(),N,XS)) -> mark(U332(isNaturalKind(N),XS))
active(U332(X1,X2)) -> U332(active(X1),X2)
active(U332(tt(),XS)) -> mark(U333(isLNat(XS),XS))
active(U333(X1,X2)) -> U333(active(X1),X2)
active(U333(tt(),XS)) -> mark(U334(isLNatKind(XS),XS))
active(U334(X1,X2)) -> U334(active(X1),X2)
active(U334(tt(),XS)) -> mark(XS)
active(U34(X1,X2)) -> U34(active(X1),X2)
active(U34(tt(),N)) -> mark(N)
active(U341(X1,X2,X3)) -> U341(active(X1),X2,X3)
active(U341(tt(),N,XS)) -> mark(U342(isNaturalKind(N),N,XS))
active(U342(X1,X2,X3)) -> U342(active(X1),X2,X3)
active(U342(tt(),N,XS)) -> mark(U343(isLNat(XS),N,XS))
active(U343(X1,X2,X3)) -> U343(active(X1),X2,X3)
active(U343(tt(),N,XS)) -> mark(U344(isLNatKind(XS),N,XS))
active(U344(X1,X2,X3)) -> U344(active(X1),X2,X3)
active(U344(tt(),N,XS)) -> mark(fst(splitAt(N,XS)))
active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
active(U41(tt(),V1,V2)) -> mark(U42(isNaturalKind(V1),V1,V2))
active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3)
active(U42(tt(),V1,V2)) -> mark(U43(isLNatKind(V2),V1,V2))
active(U43(X1,X2,X3)) -> U43(active(X1),X2,X3)
active(U43(tt(),V1,V2)) -> mark(U44(isLNatKind(V2),V1,V2))
active(U44(X1,X2,X3)) -> U44(active(X1),X2,X3)
active(U44(tt(),V1,V2)) -> mark(U45(isNatural(V1),V2))
active(U45(X1,X2)) -> U45(active(X1),X2)
active(U45(tt(),V2)) -> mark(U46(isLNat(V2)))
active(U46(X)) -> U46(active(X))
active(U46(tt())) -> mark(tt())
active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
active(U51(tt(),V1,V2)) -> mark(U52(isNaturalKind(V1),V1,V2))
active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
active(U52(tt(),V1,V2)) -> mark(U53(isLNatKind(V2),V1,V2))
active(U53(X1,X2,X3)) -> U53(active(X1),X2,X3)
active(U53(tt(),V1,V2)) -> mark(U54(isLNatKind(V2),V1,V2))
active(U54(X1,X2,X3)) -> U54(active(X1),X2,X3)
active(U54(tt(),V1,V2)) -> mark(U55(isNatural(V1),V2))
active(U55(X1,X2)) -> U55(active(X1),X2)
active(U55(tt(),V2)) -> mark(U56(isLNat(V2)))
active(U56(X)) -> U56(active(X))
active(U56(tt())) -> mark(tt())
active(U61(X1,X2)) -> U61(active(X1),X2)
active(U61(tt(),V1)) -> mark(U62(isPLNatKind(V1),V1))
active(U62(X1,X2)) -> U62(active(X1),X2)
active(U62(tt(),V1)) -> mark(U63(isPLNat(V1)))
active(U63(X)) -> U63(active(X))
active(U63(tt())) -> mark(tt())
active(U71(X1,X2)) -> U71(active(X1),X2)
active(U71(tt(),V1)) -> mark(U72(isNaturalKind(V1),V1))
active(U72(X1,X2)) -> U72(active(X1),X2)
active(U72(tt(),V1)) -> mark(U73(isNatural(V1)))
active(U73(X)) -> U73(active(X))
active(U73(tt())) -> mark(tt())
active(U81(X1,X2)) -> U81(active(X1),X2)
active(U81(tt(),V1)) -> mark(U82(isPLNatKind(V1),V1))
active(U82(X1,X2)) -> U82(active(X1),X2)
active(U82(tt(),V1)) -> mark(U83(isPLNat(V1)))
active(U83(X)) -> U83(active(X))
active(U83(tt())) -> mark(tt())
active(U91(X1,X2)) -> U91(active(X1),X2)
active(U91(tt(),V1)) -> mark(U92(isLNatKind(V1),V1))
active(U92(X1,X2)) -> U92(active(X1),X2)
active(U92(tt(),V1)) -> mark(U93(isLNat(V1)))
active(U93(X)) -> U93(active(X))
active(U93(tt())) -> mark(tt())
active(afterNth(N,XS)) -> mark(U11(isNatural(N),N,XS))
active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
active(cons(X1,X2)) -> cons(active(X1),X2)
active(fst(X)) -> fst(active(X))
active(fst(pair(X,Y))) -> mark(U21(isLNat(X),X,Y))
active(head(X)) -> head(active(X))
active(head(cons(N,XS))) -> mark(U31(isNatural(N),N,XS))
active(isLNat(afterNth(V1,V2))) -> mark(U41(isNaturalKind(V1),V1,V2))
active(isLNat(cons(V1,V2))) -> mark(U51(isNaturalKind(V1),V1,V2))
active(isLNat(fst(V1))) -> mark(U61(isPLNatKind(V1),V1))
active(isLNat(natsFrom(V1))) -> mark(U71(isNaturalKind(V1),V1))
active(isLNat(nil())) -> mark(tt())
active(isLNat(snd(V1))) -> mark(U81(isPLNatKind(V1),V1))
active(isLNat(tail(V1))) -> mark(U91(isLNatKind(V1),V1))
active(isLNat(take(V1,V2))) -> mark(U101(isNaturalKind(V1),V1,V2))
active(isLNatKind(afterNth(V1,V2))) -> mark(U111(isNaturalKind(V1),V2))
active(isLNatKind(cons(V1,V2))) -> mark(U121(isNaturalKind(V1),V2))
active(isLNatKind(fst(V1))) -> mark(U131(isPLNatKind(V1)))
active(isLNatKind(natsFrom(V1))) -> mark(U141(isNaturalKind(V1)))
active(isLNatKind(nil())) -> mark(tt())
active(isLNatKind(snd(V1))) -> mark(U151(isPLNatKind(V1)))
active(isLNatKind(tail(V1))) -> mark(U161(isLNatKind(V1)))
active(isLNatKind(take(V1,V2))) -> mark(U171(isNaturalKind(V1),V2))
active(isNatural(0())) -> mark(tt())
active(isNatural(head(V1))) -> mark(U181(isLNatKind(V1),V1))
active(isNatural(s(V1))) -> mark(U191(isNaturalKind(V1),V1))
active(isNatural(sel(V1,V2))) -> mark(U201(isNaturalKind(V1),V1,V2))
active(isNaturalKind(0())) -> mark(tt())
active(isNaturalKind(head(V1))) -> mark(U211(isLNatKind(V1)))
active(isNaturalKind(s(V1))) -> mark(U221(isNaturalKind(V1)))
active(isNaturalKind(sel(V1,V2))) -> mark(U231(isNaturalKind(V1),V2))
active(isPLNat(pair(V1,V2))) -> mark(U241(isLNatKind(V1),V1,V2))
active(isPLNat(splitAt(V1,V2))) -> mark(U251(isNaturalKind(V1),V1,V2))
active(isPLNatKind(pair(V1,V2))) -> mark(U261(isLNatKind(V1),V2))
active(isPLNatKind(splitAt(V1,V2))) -> mark(U271(isNaturalKind(V1),V2))
active(natsFrom(N)) -> mark(U281(isNatural(N),N))
active(natsFrom(X)) -> natsFrom(active(X))
active(pair(X1,X2)) -> pair(X1,active(X2))
active(pair(X1,X2)) -> pair(active(X1),X2)
active(s(X)) -> s(active(X))
active(sel(N,XS)) -> mark(U291(isNatural(N),N,XS))
active(sel(X1,X2)) -> sel(X1,active(X2))
active(sel(X1,X2)) -> sel(active(X1),X2)
active(snd(X)) -> snd(active(X))
active(snd(pair(X,Y))) -> mark(U301(isLNat(X),X,Y))
active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
active(splitAt(0(),XS)) -> mark(U311(isLNat(XS),XS))
active(splitAt(s(N),cons(X,XS))) -> mark(U321(isNatural(N),N,X,XS))
active(tail(X)) -> tail(active(X))
active(tail(cons(N,XS))) -> mark(U331(isNatural(N),N,XS))
active(take(N,XS)) -> mark(U341(isNatural(N),N,XS))
active(take(X1,X2)) -> take(X1,active(X2))
active(take(X1,X2)) -> take(active(X1),X2)
afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
cons(mark(X1),X2) -> mark(cons(X1,X2))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
fst(mark(X)) -> mark(fst(X))
fst(ok(X)) -> ok(fst(X))
head(mark(X)) -> mark(head(X))
head(ok(X)) -> ok(head(X))
isLNat(ok(X)) -> ok(isLNat(X))
isLNatKind(ok(X)) -> ok(isLNatKind(X))
isNatural(ok(X)) -> ok(isNatural(X))
isNaturalKind(ok(X)) -> ok(isNaturalKind(X))
isPLNat(ok(X)) -> ok(isPLNat(X))
isPLNatKind(ok(X)) -> ok(isPLNatKind(X))
natsFrom(mark(X)) -> mark(natsFrom(X))
natsFrom(ok(X)) -> ok(natsFrom(X))
pair(X1,mark(X2)) -> mark(pair(X1,X2))
pair(mark(X1),X2) -> mark(pair(X1,X2))
pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
proper(0()) -> ok(0())
proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
proper(U105(X1,X2)) -> U105(proper(X1),proper(X2))
proper(U106(X)) -> U106(proper(X))
proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
proper(U111(X1,X2)) -> U111(proper(X1),proper(X2))
proper(U112(X)) -> U112(proper(X))
proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
proper(U121(X1,X2)) -> U121(proper(X1),proper(X2))
proper(U122(X)) -> U122(proper(X))
proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
proper(U131(X)) -> U131(proper(X))
proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
proper(U141(X)) -> U141(proper(X))
proper(U151(X)) -> U151(proper(X))
proper(U161(X)) -> U161(proper(X))
proper(U171(X1,X2)) -> U171(proper(X1),proper(X2))
proper(U172(X)) -> U172(proper(X))
proper(U181(X1,X2)) -> U181(proper(X1),proper(X2))
proper(U182(X1,X2)) -> U182(proper(X1),proper(X2))
proper(U183(X)) -> U183(proper(X))
proper(U191(X1,X2)) -> U191(proper(X1),proper(X2))
proper(U192(X1,X2)) -> U192(proper(X1),proper(X2))
proper(U193(X)) -> U193(proper(X))
proper(U201(X1,X2,X3)) -> U201(proper(X1),proper(X2),proper(X3))
proper(U202(X1,X2,X3)) -> U202(proper(X1),proper(X2),proper(X3))
proper(U203(X1,X2,X3)) -> U203(proper(X1),proper(X2),proper(X3))
proper(U204(X1,X2,X3)) -> U204(proper(X1),proper(X2),proper(X3))
proper(U205(X1,X2)) -> U205(proper(X1),proper(X2))
proper(U206(X)) -> U206(proper(X))
proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
proper(U211(X)) -> U211(proper(X))
proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
proper(U221(X)) -> U221(proper(X))
proper(U23(X1,X2,X3)) -> U23(proper(X1),proper(X2),proper(X3))
proper(U231(X1,X2)) -> U231(proper(X1),proper(X2))
proper(U232(X)) -> U232(proper(X))
proper(U24(X1,X2)) -> U24(proper(X1),proper(X2))
proper(U241(X1,X2,X3)) -> U241(proper(X1),proper(X2),proper(X3))
proper(U242(X1,X2,X3)) -> U242(proper(X1),proper(X2),proper(X3))
proper(U243(X1,X2,X3)) -> U243(proper(X1),proper(X2),proper(X3))
proper(U244(X1,X2,X3)) -> U244(proper(X1),proper(X2),proper(X3))
proper(U245(X1,X2)) -> U245(proper(X1),proper(X2))
proper(U246(X)) -> U246(proper(X))
proper(U251(X1,X2,X3)) -> U251(proper(X1),proper(X2),proper(X3))
proper(U252(X1,X2,X3)) -> U252(proper(X1),proper(X2),proper(X3))
proper(U253(X1,X2,X3)) -> U253(proper(X1),proper(X2),proper(X3))
proper(U254(X1,X2,X3)) -> U254(proper(X1),proper(X2),proper(X3))
proper(U255(X1,X2)) -> U255(proper(X1),proper(X2))
proper(U256(X)) -> U256(proper(X))
proper(U261(X1,X2)) -> U261(proper(X1),proper(X2))
proper(U262(X)) -> U262(proper(X))
proper(U271(X1,X2)) -> U271(proper(X1),proper(X2))
proper(U272(X)) -> U272(proper(X))
proper(U281(X1,X2)) -> U281(proper(X1),proper(X2))
proper(U282(X1,X2)) -> U282(proper(X1),proper(X2))
proper(U291(X1,X2,X3)) -> U291(proper(X1),proper(X2),proper(X3))
proper(U292(X1,X2,X3)) -> U292(proper(X1),proper(X2),proper(X3))
proper(U293(X1,X2,X3)) -> U293(proper(X1),proper(X2),proper(X3))
proper(U294(X1,X2,X3)) -> U294(proper(X1),proper(X2),proper(X3))
proper(U301(X1,X2,X3)) -> U301(proper(X1),proper(X2),proper(X3))
proper(U302(X1,X2)) -> U302(proper(X1),proper(X2))
proper(U303(X1,X2)) -> U303(proper(X1),proper(X2))
proper(U304(X1,X2)) -> U304(proper(X1),proper(X2))
proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3))
proper(U311(X1,X2)) -> U311(proper(X1),proper(X2))
proper(U312(X1,X2)) -> U312(proper(X1),proper(X2))
proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3))
proper(U321(X1,X2,X3,X4)) -> U321(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U322(X1,X2,X3,X4)) -> U322(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U323(X1,X2,X3,X4)) -> U323(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U324(X1,X2,X3,X4)) -> U324(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U325(X1,X2,X3,X4)) -> U325(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U326(X1,X2,X3,X4)) -> U326(proper(X1),proper(X2),proper(X3),proper(X4))
proper(U327(X1,X2)) -> U327(proper(X1),proper(X2))
proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3))
proper(U331(X1,X2,X3)) -> U331(proper(X1),proper(X2),proper(X3))
proper(U332(X1,X2)) -> U332(proper(X1),proper(X2))
proper(U333(X1,X2)) -> U333(proper(X1),proper(X2))
proper(U334(X1,X2)) -> U334(proper(X1),proper(X2))
proper(U34(X1,X2)) -> U34(proper(X1),proper(X2))
proper(U341(X1,X2,X3)) -> U341(proper(X1),proper(X2),proper(X3))
proper(U342(X1,X2,X3)) -> U342(proper(X1),proper(X2),proper(X3))
proper(U343(X1,X2,X3)) -> U343(proper(X1),proper(X2),proper(X3))
proper(U344(X1,X2,X3)) -> U344(proper(X1),proper(X2),proper(X3))
proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3))
proper(U43(X1,X2,X3)) -> U43(proper(X1),proper(X2),proper(X3))
proper(U44(X1,X2,X3)) -> U44(proper(X1),proper(X2),proper(X3))
proper(U45(X1,X2)) -> U45(proper(X1),proper(X2))
proper(U46(X)) -> U46(proper(X))
proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
proper(U53(X1,X2,X3)) -> U53(proper(X1),proper(X2),proper(X3))
proper(U54(X1,X2,X3)) -> U54(proper(X1),proper(X2),proper(X3))
proper(U55(X1,X2)) -> U55(proper(X1),proper(X2))
proper(U56(X)) -> U56(proper(X))
proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
proper(U62(X1,X2)) -> U62(proper(X1),proper(X2))
proper(U63(X)) -> U63(proper(X))
proper(U71(X1,X2)) -> U71(proper(X1),proper(X2))
proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
proper(U73(X)) -> U73(proper(X))
proper(U81(X1,X2)) -> U81(proper(X1),proper(X2))
proper(U82(X1,X2)) -> U82(proper(X1),proper(X2))
proper(U83(X)) -> U83(proper(X))
proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
proper(U92(X1,X2)) -> U92(proper(X1),proper(X2))
proper(U93(X)) -> U93(proper(X))
proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(fst(X)) -> fst(proper(X))
proper(head(X)) -> head(proper(X))
proper(isLNat(X)) -> isLNat(proper(X))
proper(isLNatKind(X)) -> isLNatKind(proper(X))
proper(isNatural(X)) -> isNatural(proper(X))
proper(isNaturalKind(X)) -> isNaturalKind(proper(X))
proper(isPLNat(X)) -> isPLNat(proper(X))
proper(isPLNatKind(X)) -> isPLNatKind(proper(X))
proper(natsFrom(X)) -> natsFrom(proper(X))
proper(nil()) -> ok(nil())
proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
proper(s(X)) -> s(proper(X))
proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
proper(snd(X)) -> snd(proper(X))
proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
proper(tail(X)) -> tail(proper(X))
proper(take(X1,X2)) -> take(proper(X1),proper(X2))
proper(tt()) -> ok(tt())
s(mark(X)) -> mark(s(X))
s(ok(X)) -> ok(s(X))
sel(X1,mark(X2)) -> mark(sel(X1,X2))
sel(mark(X1),X2) -> mark(sel(X1,X2))
sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
snd(mark(X)) -> mark(snd(X))
snd(ok(X)) -> ok(snd(X))
splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
tail(mark(X)) -> mark(tail(X))
tail(ok(X)) -> ok(tail(X))
take(X1,mark(X2)) -> mark(take(X1,X2))
take(mark(X1),X2) -> mark(take(X1,X2))
take(ok(X1),ok(X2)) -> ok(take(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
- Signature:
{U101/3,U102/3,U103/3,U104/3,U105/2,U106/1,U11/3,U111/2,U112/1,U12/3,U121/2,U122/1,U13/3,U131/1,U14/3,U141/1
,U151/1,U161/1,U171/2,U172/1,U181/2,U182/2,U183/1,U191/2,U192/2,U193/1,U201/3,U202/3,U203/3,U204/3,U205/2
,U206/1,U21/3,U211/1,U22/3,U221/1,U23/3,U231/2,U232/1,U24/2,U241/3,U242/3,U243/3,U244/3,U245/2,U246/1,U251/3
,U252/3,U253/3,U254/3,U255/2,U256/1,U261/2,U262/1,U271/2,U272/1,U281/2,U282/2,U291/3,U292/3,U293/3,U294/3
,U301/3,U302/2,U303/2,U304/2,U31/3,U311/2,U312/2,U32/3,U321/4,U322/4,U323/4,U324/4,U325/4,U326/4,U327/2
,U33/3,U331/3,U332/2,U333/2,U334/2,U34/2,U341/3,U342/3,U343/3,U344/3,U41/3,U42/3,U43/3,U44/3,U45/2,U46/1
,U51/3,U52/3,U53/3,U54/3,U55/2,U56/1,U61/2,U62/2,U63/1,U71/2,U72/2,U73/1,U81/2,U82/2,U83/1,U91/2,U92/2,U93/1
,active/1,afterNth/2,cons/2,fst/1,head/1,isLNat/1,isLNatKind/1,isNatural/1,isNaturalKind/1,isPLNat/1
,isPLNatKind/1,natsFrom/1,pair/2,proper/1,s/1,sel/2,snd/1,splitAt/2,tail/1,take/2,top/1} / {0/0,mark/1,nil/0
,ok/1,tt/0}
- Obligation:
innermost runtime complexity wrt. defined symbols {U101,U102,U103,U104,U105,U106,U11,U111,U112,U12,U121,U122
,U13,U131,U14,U141,U151,U161,U171,U172,U181,U182,U183,U191,U192,U193,U201,U202,U203,U204,U205,U206,U21,U211
,U22,U221,U23,U231,U232,U24,U241,U242,U243,U244,U245,U246,U251,U252,U253,U254,U255,U256,U261,U262,U271,U272
,U281,U282,U291,U292,U293,U294,U301,U302,U303,U304,U31,U311,U312,U32,U321,U322,U323,U324,U325,U326,U327,U33
,U331,U332,U333,U334,U34,U341,U342,U343,U344,U41,U42,U43,U44,U45,U46,U51,U52,U53,U54,U55,U56,U61,U62,U63,U71
,U72,U73,U81,U82,U83,U91,U92,U93,active,afterNth,cons,fst,head,isLNat,isLNatKind,isNatural,isNaturalKind
,isPLNat,isPLNatKind,natsFrom,pair,proper,s,sel,snd,splitAt,tail,take,top} and constructors {0,mark,nil,ok
,tt}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
U101(x,y,z){x -> mark(x)} =
U101(mark(x),y,z) ->^+ mark(U101(x,y,z))
= C[U101(x,y,z) = U101(x,y,z){}]
WORST_CASE(Omega(n^1),?)