MPO
TIMEOUT
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), V1, V2) -> a__U102(a__isNaturalKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isLNatKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isLNatKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNatural(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isLNat(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__U12(a__isNaturalKind(N), N, XS)
, a__U111(tt(), V2) -> a__U112(a__isLNatKind(V2))
, a__U112(tt()) -> tt()
, a__U12(tt(), N, XS) -> a__U13(a__isLNat(XS), N, XS)
, a__U121(tt(), V2) -> a__U122(a__isLNatKind(V2))
, a__U122(tt()) -> tt()
, a__U13(tt(), N, XS) -> a__U14(a__isLNatKind(XS), N, XS)
, a__U131(tt()) -> tt()
, a__U14(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U141(tt()) -> tt()
, a__U151(tt()) -> tt()
, a__U161(tt()) -> tt()
, a__U171(tt(), V2) -> a__U172(a__isLNatKind(V2))
, a__U172(tt()) -> tt()
, a__U181(tt(), V1) -> a__U182(a__isLNatKind(V1), V1)
, a__U182(tt(), V1) -> a__U183(a__isLNat(V1))
, a__U183(tt()) -> tt()
, a__U191(tt(), V1) -> a__U192(a__isNaturalKind(V1), V1)
, a__U192(tt(), V1) -> a__U193(a__isNatural(V1))
, a__U193(tt()) -> tt()
, a__U201(tt(), V1, V2) -> a__U202(a__isNaturalKind(V1), V1, V2)
, a__U202(tt(), V1, V2) -> a__U203(a__isLNatKind(V2), V1, V2)
, a__U203(tt(), V1, V2) -> a__U204(a__isLNatKind(V2), V1, V2)
, a__U204(tt(), V1, V2) -> a__U205(a__isNatural(V1), V2)
, a__U205(tt(), V2) -> a__U206(a__isLNat(V2))
, a__U206(tt()) -> tt()
, a__U21(tt(), X, Y) -> a__U22(a__isLNatKind(X), X, Y)
, a__U211(tt()) -> tt()
, a__U22(tt(), X, Y) -> a__U23(a__isLNat(Y), X, Y)
, a__U221(tt()) -> tt()
, a__U23(tt(), X, Y) -> a__U24(a__isLNatKind(Y), X)
, a__U231(tt(), V2) -> a__U232(a__isLNatKind(V2))
, a__U232(tt()) -> tt()
, a__U24(tt(), X) -> mark(X)
, a__U241(tt(), V1, V2) -> a__U242(a__isLNatKind(V1), V1, V2)
, a__U242(tt(), V1, V2) -> a__U243(a__isLNatKind(V2), V1, V2)
, a__U243(tt(), V1, V2) -> a__U244(a__isLNatKind(V2), V1, V2)
, a__U244(tt(), V1, V2) -> a__U245(a__isLNat(V1), V2)
, a__U245(tt(), V2) -> a__U246(a__isLNat(V2))
, a__U246(tt()) -> tt()
, a__U251(tt(), V1, V2) -> a__U252(a__isNaturalKind(V1), V1, V2)
, a__U252(tt(), V1, V2) -> a__U253(a__isLNatKind(V2), V1, V2)
, a__U253(tt(), V1, V2) -> a__U254(a__isLNatKind(V2), V1, V2)
, a__U254(tt(), V1, V2) -> a__U255(a__isNatural(V1), V2)
, a__U255(tt(), V2) -> a__U256(a__isLNat(V2))
, a__U256(tt()) -> tt()
, a__U261(tt(), V2) -> a__U262(a__isLNatKind(V2))
, a__U262(tt()) -> tt()
, a__U271(tt(), V2) -> a__U272(a__isLNatKind(V2))
, a__U272(tt()) -> tt()
, a__U281(tt(), N) -> a__U282(a__isNaturalKind(N), N)
, a__U282(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U291(tt(), N, XS) -> a__U292(a__isNaturalKind(N), N, XS)
, a__U292(tt(), N, XS) -> a__U293(a__isLNat(XS), N, XS)
, a__U293(tt(), N, XS) -> a__U294(a__isLNatKind(XS), N, XS)
, a__U294(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U301(tt(), X, Y) -> a__U302(a__isLNatKind(X), Y)
, a__U302(tt(), Y) -> a__U303(a__isLNat(Y), Y)
, a__U303(tt(), Y) -> a__U304(a__isLNatKind(Y), Y)
, a__U304(tt(), Y) -> mark(Y)
, a__U31(tt(), N, XS) -> a__U32(a__isNaturalKind(N), N, XS)
, a__U311(tt(), XS) -> a__U312(a__isLNatKind(XS), XS)
, a__U312(tt(), XS) -> pair(nil(), mark(XS))
, a__U32(tt(), N, XS) -> a__U33(a__isLNat(XS), N, XS)
, a__U321(tt(), N, X, XS) -> a__U322(a__isNaturalKind(N), N, X, XS)
, a__U322(tt(), N, X, XS) -> a__U323(a__isNatural(X), N, X, XS)
, a__U323(tt(), N, X, XS) -> a__U324(a__isNaturalKind(X), N, X, XS)
, a__U324(tt(), N, X, XS) -> a__U325(a__isLNat(XS), N, X, XS)
, a__U325(tt(), N, X, XS) -> a__U326(a__isLNatKind(XS), N, X, XS)
, a__U326(tt(), N, X, XS) ->
a__U327(a__splitAt(mark(N), mark(XS)), X)
, a__U327(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U33(tt(), N, XS) -> a__U34(a__isLNatKind(XS), N)
, a__U331(tt(), N, XS) -> a__U332(a__isNaturalKind(N), XS)
, a__U332(tt(), XS) -> a__U333(a__isLNat(XS), XS)
, a__U333(tt(), XS) -> a__U334(a__isLNatKind(XS), XS)
, a__U334(tt(), XS) -> mark(XS)
, a__U34(tt(), N) -> mark(N)
, a__U341(tt(), N, XS) -> a__U342(a__isNaturalKind(N), N, XS)
, a__U342(tt(), N, XS) -> a__U343(a__isLNat(XS), N, XS)
, a__U343(tt(), N, XS) -> a__U344(a__isLNatKind(XS), N, XS)
, a__U344(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U41(tt(), V1, V2) -> a__U42(a__isNaturalKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isLNatKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isLNatKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNatural(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isLNat(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNaturalKind(V1), V1, V2)
, a__U52(tt(), V1, V2) -> a__U53(a__isLNatKind(V2), V1, V2)
, a__U53(tt(), V1, V2) -> a__U54(a__isLNatKind(V2), V1, V2)
, a__U54(tt(), V1, V2) -> a__U55(a__isNatural(V1), V2)
, a__U55(tt(), V2) -> a__U56(a__isLNat(V2))
, a__U56(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNatKind(V1), V1)
, a__U62(tt(), V1) -> a__U63(a__isPLNat(V1))
, a__U63(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNaturalKind(V1), V1)
, a__U72(tt(), V1) -> a__U73(a__isNatural(V1))
, a__U73(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNatKind(V1), V1)
, a__U82(tt(), V1) -> a__U83(a__isPLNat(V1))
, a__U83(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNatKind(V1), V1)
, a__U92(tt(), V1) -> a__U93(a__isLNat(V1))
, a__U93(tt()) -> tt()
, a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
, a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
, a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__isNaturalKind(V1), V1, V2)
, a__isLNat(cons(V1, V2)) -> a__U51(a__isNaturalKind(V1), V1, V2)
, a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1)
, a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1)
, a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1)
, a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1)
, a__isLNat(take(V1, V2)) -> a__U101(a__isNaturalKind(V1), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__U111(a__isNaturalKind(V1), V2)
, a__isLNatKind(cons(V1, V2)) -> a__U121(a__isNaturalKind(V1), V2)
, a__isLNatKind(fst(V1)) -> a__U131(a__isPLNatKind(V1))
, a__isLNatKind(natsFrom(V1)) -> a__U141(a__isNaturalKind(V1))
, a__isLNatKind(snd(V1)) -> a__U151(a__isPLNatKind(V1))
, a__isLNatKind(tail(V1)) -> a__U161(a__isLNatKind(V1))
, a__isLNatKind(take(V1, V2)) -> a__U171(a__isNaturalKind(V1), V2)
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U181(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U191(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U201(a__isNaturalKind(V1), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__U211(a__isLNatKind(V1))
, a__isNaturalKind(s(V1)) -> a__U221(a__isNaturalKind(V1))
, a__isNaturalKind(sel(V1, V2)) ->
a__U231(a__isNaturalKind(V1), V2)
, a__isPLNat(pair(V1, V2)) -> a__U241(a__isLNatKind(V1), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U251(a__isNaturalKind(V1), V1, V2)
, a__isPLNatKind(pair(V1, V2)) -> a__U261(a__isLNatKind(V1), V2)
, a__isPLNatKind(splitAt(V1, V2)) ->
a__U271(a__isNaturalKind(V1), V2)
, a__natsFrom(N) -> a__U281(a__isNatural(N), N)
, a__sel(N, XS) -> a__U291(a__isNatural(N), N, XS)
, a__snd(pair(X, Y)) -> a__U301(a__isLNat(X), X, Y)
, a__splitAt(0(), XS) -> a__U311(a__isLNat(XS), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U321(a__isNatural(N), N, X, XS)
, a__tail(cons(N, XS)) -> a__U331(a__isNatural(N), N, XS)
, a__take(N, XS) -> a__U341(a__isNatural(N), N, XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U131(X)) -> a__U131(mark(X))
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U141(X)) -> a__U141(mark(X))
, mark(U151(X)) -> a__U151(mark(X))
, mark(U161(X)) -> a__U161(mark(X))
, mark(U171(X1, X2)) -> a__U171(mark(X1), X2)
, mark(U172(X)) -> a__U172(mark(X))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U182(X1, X2)) -> a__U182(mark(X1), X2)
, mark(U183(X)) -> a__U183(mark(X))
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U192(X1, X2)) -> a__U192(mark(X1), X2)
, mark(U193(X)) -> a__U193(mark(X))
, mark(U201(X1, X2, X3)) -> a__U201(mark(X1), X2, X3)
, mark(U202(X1, X2, X3)) -> a__U202(mark(X1), X2, X3)
, mark(U203(X1, X2, X3)) -> a__U203(mark(X1), X2, X3)
, mark(U204(X1, X2, X3)) -> a__U204(mark(X1), X2, X3)
, mark(U205(X1, X2)) -> a__U205(mark(X1), X2)
, mark(U206(X)) -> a__U206(mark(X))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(U211(X)) -> a__U211(mark(X))
, mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
, mark(U221(X)) -> a__U221(mark(X))
, mark(U24(X1, X2)) -> a__U24(mark(X1), X2)
, mark(U231(X1, X2)) -> a__U231(mark(X1), X2)
, mark(U232(X)) -> a__U232(mark(X))
, mark(U241(X1, X2, X3)) -> a__U241(mark(X1), X2, X3)
, mark(U242(X1, X2, X3)) -> a__U242(mark(X1), X2, X3)
, mark(U243(X1, X2, X3)) -> a__U243(mark(X1), X2, X3)
, mark(U244(X1, X2, X3)) -> a__U244(mark(X1), X2, X3)
, mark(U245(X1, X2)) -> a__U245(mark(X1), X2)
, mark(U246(X)) -> a__U246(mark(X))
, mark(U251(X1, X2, X3)) -> a__U251(mark(X1), X2, X3)
, mark(U252(X1, X2, X3)) -> a__U252(mark(X1), X2, X3)
, mark(U253(X1, X2, X3)) -> a__U253(mark(X1), X2, X3)
, mark(U254(X1, X2, X3)) -> a__U254(mark(X1), X2, X3)
, mark(U255(X1, X2)) -> a__U255(mark(X1), X2)
, mark(U256(X)) -> a__U256(mark(X))
, mark(U261(X1, X2)) -> a__U261(mark(X1), X2)
, mark(U262(X)) -> a__U262(mark(X))
, mark(U271(X1, X2)) -> a__U271(mark(X1), X2)
, mark(U272(X)) -> a__U272(mark(X))
, mark(U281(X1, X2)) -> a__U281(mark(X1), X2)
, mark(U282(X1, X2)) -> a__U282(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U291(X1, X2, X3)) -> a__U291(mark(X1), X2, X3)
, mark(U292(X1, X2, X3)) -> a__U292(mark(X1), X2, X3)
, mark(U293(X1, X2, X3)) -> a__U293(mark(X1), X2, X3)
, mark(U294(X1, X2, X3)) -> a__U294(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U301(X1, X2, X3)) -> a__U301(mark(X1), X2, X3)
, mark(U302(X1, X2)) -> a__U302(mark(X1), X2)
, mark(U303(X1, X2)) -> a__U303(mark(X1), X2)
, mark(U304(X1, X2)) -> a__U304(mark(X1), X2)
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U311(X1, X2)) -> a__U311(mark(X1), X2)
, mark(U312(X1, X2)) -> a__U312(mark(X1), X2)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U321(X1, X2, X3, X4)) -> a__U321(mark(X1), X2, X3, X4)
, mark(U322(X1, X2, X3, X4)) -> a__U322(mark(X1), X2, X3, X4)
, mark(U323(X1, X2, X3, X4)) -> a__U323(mark(X1), X2, X3, X4)
, mark(U324(X1, X2, X3, X4)) -> a__U324(mark(X1), X2, X3, X4)
, mark(U325(X1, X2, X3, X4)) -> a__U325(mark(X1), X2, X3, X4)
, mark(U326(X1, X2, X3, X4)) -> a__U326(mark(X1), X2, X3, X4)
, mark(U327(X1, X2)) -> a__U327(mark(X1), X2)
, mark(U34(X1, X2)) -> a__U34(mark(X1), X2)
, mark(U331(X1, X2, X3)) -> a__U331(mark(X1), X2, X3)
, mark(U332(X1, X2)) -> a__U332(mark(X1), X2)
, mark(U333(X1, X2)) -> a__U333(mark(X1), X2)
, mark(U334(X1, X2)) -> a__U334(mark(X1), X2)
, mark(U341(X1, X2, X3)) -> a__U341(mark(X1), X2, X3)
, mark(U342(X1, X2, X3)) -> a__U342(mark(X1), X2, X3)
, mark(U343(X1, X2, X3)) -> a__U343(mark(X1), X2, X3)
, mark(U344(X1, X2, X3)) -> a__U344(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
, mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
, mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
, mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
, mark(U56(X)) -> a__U56(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(isPLNatKind(X)) -> a__isPLNatKind(X)
, mark(U63(X)) -> a__U63(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U73(X)) -> a__U73(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
, mark(U83(X)) -> a__U83(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X1, X2)) -> a__U92(mark(X1), X2)
, mark(U93(X)) -> a__U93(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, mark(nil()) -> nil()
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isLNatKind(X) -> isLNatKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U106(X) -> U106(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U131(X) -> U131(X)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U141(X) -> U141(X)
, a__U151(X) -> U151(X)
, a__U161(X) -> U161(X)
, a__U171(X1, X2) -> U171(X1, X2)
, a__U172(X) -> U172(X)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U182(X1, X2) -> U182(X1, X2)
, a__U183(X) -> U183(X)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U192(X1, X2) -> U192(X1, X2)
, a__U193(X) -> U193(X)
, a__U201(X1, X2, X3) -> U201(X1, X2, X3)
, a__U202(X1, X2, X3) -> U202(X1, X2, X3)
, a__U203(X1, X2, X3) -> U203(X1, X2, X3)
, a__U204(X1, X2, X3) -> U204(X1, X2, X3)
, a__U205(X1, X2) -> U205(X1, X2)
, a__U206(X) -> U206(X)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__U211(X) -> U211(X)
, a__U23(X1, X2, X3) -> U23(X1, X2, X3)
, a__U221(X) -> U221(X)
, a__U24(X1, X2) -> U24(X1, X2)
, a__U231(X1, X2) -> U231(X1, X2)
, a__U232(X) -> U232(X)
, a__U241(X1, X2, X3) -> U241(X1, X2, X3)
, a__U242(X1, X2, X3) -> U242(X1, X2, X3)
, a__U243(X1, X2, X3) -> U243(X1, X2, X3)
, a__U244(X1, X2, X3) -> U244(X1, X2, X3)
, a__U245(X1, X2) -> U245(X1, X2)
, a__U246(X) -> U246(X)
, a__U251(X1, X2, X3) -> U251(X1, X2, X3)
, a__U252(X1, X2, X3) -> U252(X1, X2, X3)
, a__U253(X1, X2, X3) -> U253(X1, X2, X3)
, a__U254(X1, X2, X3) -> U254(X1, X2, X3)
, a__U255(X1, X2) -> U255(X1, X2)
, a__U256(X) -> U256(X)
, a__U261(X1, X2) -> U261(X1, X2)
, a__U262(X) -> U262(X)
, a__U271(X1, X2) -> U271(X1, X2)
, a__U272(X) -> U272(X)
, a__U281(X1, X2) -> U281(X1, X2)
, a__U282(X1, X2) -> U282(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U291(X1, X2, X3) -> U291(X1, X2, X3)
, a__U292(X1, X2, X3) -> U292(X1, X2, X3)
, a__U293(X1, X2, X3) -> U293(X1, X2, X3)
, a__U294(X1, X2, X3) -> U294(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U301(X1, X2, X3) -> U301(X1, X2, X3)
, a__U302(X1, X2) -> U302(X1, X2)
, a__U303(X1, X2) -> U303(X1, X2)
, a__U304(X1, X2) -> U304(X1, X2)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U311(X1, X2) -> U311(X1, X2)
, a__U312(X1, X2) -> U312(X1, X2)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U321(X1, X2, X3, X4) -> U321(X1, X2, X3, X4)
, a__U322(X1, X2, X3, X4) -> U322(X1, X2, X3, X4)
, a__U323(X1, X2, X3, X4) -> U323(X1, X2, X3, X4)
, a__U324(X1, X2, X3, X4) -> U324(X1, X2, X3, X4)
, a__U325(X1, X2, X3, X4) -> U325(X1, X2, X3, X4)
, a__U326(X1, X2, X3, X4) -> U326(X1, X2, X3, X4)
, a__U327(X1, X2) -> U327(X1, X2)
, a__U34(X1, X2) -> U34(X1, X2)
, a__U331(X1, X2, X3) -> U331(X1, X2, X3)
, a__U332(X1, X2) -> U332(X1, X2)
, a__U333(X1, X2) -> U333(X1, X2)
, a__U334(X1, X2) -> U334(X1, X2)
, a__U341(X1, X2, X3) -> U341(X1, X2, X3)
, a__U342(X1, X2, X3) -> U342(X1, X2, X3)
, a__U343(X1, X2, X3) -> U343(X1, X2, X3)
, a__U344(X1, X2, X3) -> U344(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2, X3) -> U52(X1, X2, X3)
, a__U53(X1, X2, X3) -> U53(X1, X2, X3)
, a__U54(X1, X2, X3) -> U54(X1, X2, X3)
, a__U55(X1, X2) -> U55(X1, X2)
, a__U56(X) -> U56(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X1, X2) -> U62(X1, X2)
, a__isPLNatKind(X) -> isPLNatKind(X)
, a__U63(X) -> U63(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U73(X) -> U73(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X1, X2) -> U82(X1, X2)
, a__U83(X) -> U83(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X1, X2) -> U92(X1, X2)
, a__U93(X) -> U93(X)
, a__tail(X) -> tail(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 6.0e-5 seconds.
Arrrr..
POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), V1, V2) -> a__U102(a__isNaturalKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isLNatKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isLNatKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNatural(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isLNat(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__U12(a__isNaturalKind(N), N, XS)
, a__U111(tt(), V2) -> a__U112(a__isLNatKind(V2))
, a__U112(tt()) -> tt()
, a__U12(tt(), N, XS) -> a__U13(a__isLNat(XS), N, XS)
, a__U121(tt(), V2) -> a__U122(a__isLNatKind(V2))
, a__U122(tt()) -> tt()
, a__U13(tt(), N, XS) -> a__U14(a__isLNatKind(XS), N, XS)
, a__U131(tt()) -> tt()
, a__U14(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U141(tt()) -> tt()
, a__U151(tt()) -> tt()
, a__U161(tt()) -> tt()
, a__U171(tt(), V2) -> a__U172(a__isLNatKind(V2))
, a__U172(tt()) -> tt()
, a__U181(tt(), V1) -> a__U182(a__isLNatKind(V1), V1)
, a__U182(tt(), V1) -> a__U183(a__isLNat(V1))
, a__U183(tt()) -> tt()
, a__U191(tt(), V1) -> a__U192(a__isNaturalKind(V1), V1)
, a__U192(tt(), V1) -> a__U193(a__isNatural(V1))
, a__U193(tt()) -> tt()
, a__U201(tt(), V1, V2) -> a__U202(a__isNaturalKind(V1), V1, V2)
, a__U202(tt(), V1, V2) -> a__U203(a__isLNatKind(V2), V1, V2)
, a__U203(tt(), V1, V2) -> a__U204(a__isLNatKind(V2), V1, V2)
, a__U204(tt(), V1, V2) -> a__U205(a__isNatural(V1), V2)
, a__U205(tt(), V2) -> a__U206(a__isLNat(V2))
, a__U206(tt()) -> tt()
, a__U21(tt(), X, Y) -> a__U22(a__isLNatKind(X), X, Y)
, a__U211(tt()) -> tt()
, a__U22(tt(), X, Y) -> a__U23(a__isLNat(Y), X, Y)
, a__U221(tt()) -> tt()
, a__U23(tt(), X, Y) -> a__U24(a__isLNatKind(Y), X)
, a__U231(tt(), V2) -> a__U232(a__isLNatKind(V2))
, a__U232(tt()) -> tt()
, a__U24(tt(), X) -> mark(X)
, a__U241(tt(), V1, V2) -> a__U242(a__isLNatKind(V1), V1, V2)
, a__U242(tt(), V1, V2) -> a__U243(a__isLNatKind(V2), V1, V2)
, a__U243(tt(), V1, V2) -> a__U244(a__isLNatKind(V2), V1, V2)
, a__U244(tt(), V1, V2) -> a__U245(a__isLNat(V1), V2)
, a__U245(tt(), V2) -> a__U246(a__isLNat(V2))
, a__U246(tt()) -> tt()
, a__U251(tt(), V1, V2) -> a__U252(a__isNaturalKind(V1), V1, V2)
, a__U252(tt(), V1, V2) -> a__U253(a__isLNatKind(V2), V1, V2)
, a__U253(tt(), V1, V2) -> a__U254(a__isLNatKind(V2), V1, V2)
, a__U254(tt(), V1, V2) -> a__U255(a__isNatural(V1), V2)
, a__U255(tt(), V2) -> a__U256(a__isLNat(V2))
, a__U256(tt()) -> tt()
, a__U261(tt(), V2) -> a__U262(a__isLNatKind(V2))
, a__U262(tt()) -> tt()
, a__U271(tt(), V2) -> a__U272(a__isLNatKind(V2))
, a__U272(tt()) -> tt()
, a__U281(tt(), N) -> a__U282(a__isNaturalKind(N), N)
, a__U282(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U291(tt(), N, XS) -> a__U292(a__isNaturalKind(N), N, XS)
, a__U292(tt(), N, XS) -> a__U293(a__isLNat(XS), N, XS)
, a__U293(tt(), N, XS) -> a__U294(a__isLNatKind(XS), N, XS)
, a__U294(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U301(tt(), X, Y) -> a__U302(a__isLNatKind(X), Y)
, a__U302(tt(), Y) -> a__U303(a__isLNat(Y), Y)
, a__U303(tt(), Y) -> a__U304(a__isLNatKind(Y), Y)
, a__U304(tt(), Y) -> mark(Y)
, a__U31(tt(), N, XS) -> a__U32(a__isNaturalKind(N), N, XS)
, a__U311(tt(), XS) -> a__U312(a__isLNatKind(XS), XS)
, a__U312(tt(), XS) -> pair(nil(), mark(XS))
, a__U32(tt(), N, XS) -> a__U33(a__isLNat(XS), N, XS)
, a__U321(tt(), N, X, XS) -> a__U322(a__isNaturalKind(N), N, X, XS)
, a__U322(tt(), N, X, XS) -> a__U323(a__isNatural(X), N, X, XS)
, a__U323(tt(), N, X, XS) -> a__U324(a__isNaturalKind(X), N, X, XS)
, a__U324(tt(), N, X, XS) -> a__U325(a__isLNat(XS), N, X, XS)
, a__U325(tt(), N, X, XS) -> a__U326(a__isLNatKind(XS), N, X, XS)
, a__U326(tt(), N, X, XS) ->
a__U327(a__splitAt(mark(N), mark(XS)), X)
, a__U327(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U33(tt(), N, XS) -> a__U34(a__isLNatKind(XS), N)
, a__U331(tt(), N, XS) -> a__U332(a__isNaturalKind(N), XS)
, a__U332(tt(), XS) -> a__U333(a__isLNat(XS), XS)
, a__U333(tt(), XS) -> a__U334(a__isLNatKind(XS), XS)
, a__U334(tt(), XS) -> mark(XS)
, a__U34(tt(), N) -> mark(N)
, a__U341(tt(), N, XS) -> a__U342(a__isNaturalKind(N), N, XS)
, a__U342(tt(), N, XS) -> a__U343(a__isLNat(XS), N, XS)
, a__U343(tt(), N, XS) -> a__U344(a__isLNatKind(XS), N, XS)
, a__U344(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U41(tt(), V1, V2) -> a__U42(a__isNaturalKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isLNatKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isLNatKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNatural(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isLNat(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNaturalKind(V1), V1, V2)
, a__U52(tt(), V1, V2) -> a__U53(a__isLNatKind(V2), V1, V2)
, a__U53(tt(), V1, V2) -> a__U54(a__isLNatKind(V2), V1, V2)
, a__U54(tt(), V1, V2) -> a__U55(a__isNatural(V1), V2)
, a__U55(tt(), V2) -> a__U56(a__isLNat(V2))
, a__U56(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNatKind(V1), V1)
, a__U62(tt(), V1) -> a__U63(a__isPLNat(V1))
, a__U63(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNaturalKind(V1), V1)
, a__U72(tt(), V1) -> a__U73(a__isNatural(V1))
, a__U73(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNatKind(V1), V1)
, a__U82(tt(), V1) -> a__U83(a__isPLNat(V1))
, a__U83(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNatKind(V1), V1)
, a__U92(tt(), V1) -> a__U93(a__isLNat(V1))
, a__U93(tt()) -> tt()
, a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
, a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
, a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__isNaturalKind(V1), V1, V2)
, a__isLNat(cons(V1, V2)) -> a__U51(a__isNaturalKind(V1), V1, V2)
, a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1)
, a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1)
, a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1)
, a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1)
, a__isLNat(take(V1, V2)) -> a__U101(a__isNaturalKind(V1), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__U111(a__isNaturalKind(V1), V2)
, a__isLNatKind(cons(V1, V2)) -> a__U121(a__isNaturalKind(V1), V2)
, a__isLNatKind(fst(V1)) -> a__U131(a__isPLNatKind(V1))
, a__isLNatKind(natsFrom(V1)) -> a__U141(a__isNaturalKind(V1))
, a__isLNatKind(snd(V1)) -> a__U151(a__isPLNatKind(V1))
, a__isLNatKind(tail(V1)) -> a__U161(a__isLNatKind(V1))
, a__isLNatKind(take(V1, V2)) -> a__U171(a__isNaturalKind(V1), V2)
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U181(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U191(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U201(a__isNaturalKind(V1), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__U211(a__isLNatKind(V1))
, a__isNaturalKind(s(V1)) -> a__U221(a__isNaturalKind(V1))
, a__isNaturalKind(sel(V1, V2)) ->
a__U231(a__isNaturalKind(V1), V2)
, a__isPLNat(pair(V1, V2)) -> a__U241(a__isLNatKind(V1), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U251(a__isNaturalKind(V1), V1, V2)
, a__isPLNatKind(pair(V1, V2)) -> a__U261(a__isLNatKind(V1), V2)
, a__isPLNatKind(splitAt(V1, V2)) ->
a__U271(a__isNaturalKind(V1), V2)
, a__natsFrom(N) -> a__U281(a__isNatural(N), N)
, a__sel(N, XS) -> a__U291(a__isNatural(N), N, XS)
, a__snd(pair(X, Y)) -> a__U301(a__isLNat(X), X, Y)
, a__splitAt(0(), XS) -> a__U311(a__isLNat(XS), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U321(a__isNatural(N), N, X, XS)
, a__tail(cons(N, XS)) -> a__U331(a__isNatural(N), N, XS)
, a__take(N, XS) -> a__U341(a__isNatural(N), N, XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U131(X)) -> a__U131(mark(X))
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U141(X)) -> a__U141(mark(X))
, mark(U151(X)) -> a__U151(mark(X))
, mark(U161(X)) -> a__U161(mark(X))
, mark(U171(X1, X2)) -> a__U171(mark(X1), X2)
, mark(U172(X)) -> a__U172(mark(X))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U182(X1, X2)) -> a__U182(mark(X1), X2)
, mark(U183(X)) -> a__U183(mark(X))
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U192(X1, X2)) -> a__U192(mark(X1), X2)
, mark(U193(X)) -> a__U193(mark(X))
, mark(U201(X1, X2, X3)) -> a__U201(mark(X1), X2, X3)
, mark(U202(X1, X2, X3)) -> a__U202(mark(X1), X2, X3)
, mark(U203(X1, X2, X3)) -> a__U203(mark(X1), X2, X3)
, mark(U204(X1, X2, X3)) -> a__U204(mark(X1), X2, X3)
, mark(U205(X1, X2)) -> a__U205(mark(X1), X2)
, mark(U206(X)) -> a__U206(mark(X))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(U211(X)) -> a__U211(mark(X))
, mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
, mark(U221(X)) -> a__U221(mark(X))
, mark(U24(X1, X2)) -> a__U24(mark(X1), X2)
, mark(U231(X1, X2)) -> a__U231(mark(X1), X2)
, mark(U232(X)) -> a__U232(mark(X))
, mark(U241(X1, X2, X3)) -> a__U241(mark(X1), X2, X3)
, mark(U242(X1, X2, X3)) -> a__U242(mark(X1), X2, X3)
, mark(U243(X1, X2, X3)) -> a__U243(mark(X1), X2, X3)
, mark(U244(X1, X2, X3)) -> a__U244(mark(X1), X2, X3)
, mark(U245(X1, X2)) -> a__U245(mark(X1), X2)
, mark(U246(X)) -> a__U246(mark(X))
, mark(U251(X1, X2, X3)) -> a__U251(mark(X1), X2, X3)
, mark(U252(X1, X2, X3)) -> a__U252(mark(X1), X2, X3)
, mark(U253(X1, X2, X3)) -> a__U253(mark(X1), X2, X3)
, mark(U254(X1, X2, X3)) -> a__U254(mark(X1), X2, X3)
, mark(U255(X1, X2)) -> a__U255(mark(X1), X2)
, mark(U256(X)) -> a__U256(mark(X))
, mark(U261(X1, X2)) -> a__U261(mark(X1), X2)
, mark(U262(X)) -> a__U262(mark(X))
, mark(U271(X1, X2)) -> a__U271(mark(X1), X2)
, mark(U272(X)) -> a__U272(mark(X))
, mark(U281(X1, X2)) -> a__U281(mark(X1), X2)
, mark(U282(X1, X2)) -> a__U282(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U291(X1, X2, X3)) -> a__U291(mark(X1), X2, X3)
, mark(U292(X1, X2, X3)) -> a__U292(mark(X1), X2, X3)
, mark(U293(X1, X2, X3)) -> a__U293(mark(X1), X2, X3)
, mark(U294(X1, X2, X3)) -> a__U294(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U301(X1, X2, X3)) -> a__U301(mark(X1), X2, X3)
, mark(U302(X1, X2)) -> a__U302(mark(X1), X2)
, mark(U303(X1, X2)) -> a__U303(mark(X1), X2)
, mark(U304(X1, X2)) -> a__U304(mark(X1), X2)
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U311(X1, X2)) -> a__U311(mark(X1), X2)
, mark(U312(X1, X2)) -> a__U312(mark(X1), X2)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U321(X1, X2, X3, X4)) -> a__U321(mark(X1), X2, X3, X4)
, mark(U322(X1, X2, X3, X4)) -> a__U322(mark(X1), X2, X3, X4)
, mark(U323(X1, X2, X3, X4)) -> a__U323(mark(X1), X2, X3, X4)
, mark(U324(X1, X2, X3, X4)) -> a__U324(mark(X1), X2, X3, X4)
, mark(U325(X1, X2, X3, X4)) -> a__U325(mark(X1), X2, X3, X4)
, mark(U326(X1, X2, X3, X4)) -> a__U326(mark(X1), X2, X3, X4)
, mark(U327(X1, X2)) -> a__U327(mark(X1), X2)
, mark(U34(X1, X2)) -> a__U34(mark(X1), X2)
, mark(U331(X1, X2, X3)) -> a__U331(mark(X1), X2, X3)
, mark(U332(X1, X2)) -> a__U332(mark(X1), X2)
, mark(U333(X1, X2)) -> a__U333(mark(X1), X2)
, mark(U334(X1, X2)) -> a__U334(mark(X1), X2)
, mark(U341(X1, X2, X3)) -> a__U341(mark(X1), X2, X3)
, mark(U342(X1, X2, X3)) -> a__U342(mark(X1), X2, X3)
, mark(U343(X1, X2, X3)) -> a__U343(mark(X1), X2, X3)
, mark(U344(X1, X2, X3)) -> a__U344(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
, mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
, mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
, mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
, mark(U56(X)) -> a__U56(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(isPLNatKind(X)) -> a__isPLNatKind(X)
, mark(U63(X)) -> a__U63(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U73(X)) -> a__U73(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
, mark(U83(X)) -> a__U83(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X1, X2)) -> a__U92(mark(X1), X2)
, mark(U93(X)) -> a__U93(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, mark(nil()) -> nil()
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isLNatKind(X) -> isLNatKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U106(X) -> U106(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U131(X) -> U131(X)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U141(X) -> U141(X)
, a__U151(X) -> U151(X)
, a__U161(X) -> U161(X)
, a__U171(X1, X2) -> U171(X1, X2)
, a__U172(X) -> U172(X)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U182(X1, X2) -> U182(X1, X2)
, a__U183(X) -> U183(X)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U192(X1, X2) -> U192(X1, X2)
, a__U193(X) -> U193(X)
, a__U201(X1, X2, X3) -> U201(X1, X2, X3)
, a__U202(X1, X2, X3) -> U202(X1, X2, X3)
, a__U203(X1, X2, X3) -> U203(X1, X2, X3)
, a__U204(X1, X2, X3) -> U204(X1, X2, X3)
, a__U205(X1, X2) -> U205(X1, X2)
, a__U206(X) -> U206(X)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__U211(X) -> U211(X)
, a__U23(X1, X2, X3) -> U23(X1, X2, X3)
, a__U221(X) -> U221(X)
, a__U24(X1, X2) -> U24(X1, X2)
, a__U231(X1, X2) -> U231(X1, X2)
, a__U232(X) -> U232(X)
, a__U241(X1, X2, X3) -> U241(X1, X2, X3)
, a__U242(X1, X2, X3) -> U242(X1, X2, X3)
, a__U243(X1, X2, X3) -> U243(X1, X2, X3)
, a__U244(X1, X2, X3) -> U244(X1, X2, X3)
, a__U245(X1, X2) -> U245(X1, X2)
, a__U246(X) -> U246(X)
, a__U251(X1, X2, X3) -> U251(X1, X2, X3)
, a__U252(X1, X2, X3) -> U252(X1, X2, X3)
, a__U253(X1, X2, X3) -> U253(X1, X2, X3)
, a__U254(X1, X2, X3) -> U254(X1, X2, X3)
, a__U255(X1, X2) -> U255(X1, X2)
, a__U256(X) -> U256(X)
, a__U261(X1, X2) -> U261(X1, X2)
, a__U262(X) -> U262(X)
, a__U271(X1, X2) -> U271(X1, X2)
, a__U272(X) -> U272(X)
, a__U281(X1, X2) -> U281(X1, X2)
, a__U282(X1, X2) -> U282(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U291(X1, X2, X3) -> U291(X1, X2, X3)
, a__U292(X1, X2, X3) -> U292(X1, X2, X3)
, a__U293(X1, X2, X3) -> U293(X1, X2, X3)
, a__U294(X1, X2, X3) -> U294(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U301(X1, X2, X3) -> U301(X1, X2, X3)
, a__U302(X1, X2) -> U302(X1, X2)
, a__U303(X1, X2) -> U303(X1, X2)
, a__U304(X1, X2) -> U304(X1, X2)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U311(X1, X2) -> U311(X1, X2)
, a__U312(X1, X2) -> U312(X1, X2)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U321(X1, X2, X3, X4) -> U321(X1, X2, X3, X4)
, a__U322(X1, X2, X3, X4) -> U322(X1, X2, X3, X4)
, a__U323(X1, X2, X3, X4) -> U323(X1, X2, X3, X4)
, a__U324(X1, X2, X3, X4) -> U324(X1, X2, X3, X4)
, a__U325(X1, X2, X3, X4) -> U325(X1, X2, X3, X4)
, a__U326(X1, X2, X3, X4) -> U326(X1, X2, X3, X4)
, a__U327(X1, X2) -> U327(X1, X2)
, a__U34(X1, X2) -> U34(X1, X2)
, a__U331(X1, X2, X3) -> U331(X1, X2, X3)
, a__U332(X1, X2) -> U332(X1, X2)
, a__U333(X1, X2) -> U333(X1, X2)
, a__U334(X1, X2) -> U334(X1, X2)
, a__U341(X1, X2, X3) -> U341(X1, X2, X3)
, a__U342(X1, X2, X3) -> U342(X1, X2, X3)
, a__U343(X1, X2, X3) -> U343(X1, X2, X3)
, a__U344(X1, X2, X3) -> U344(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2, X3) -> U52(X1, X2, X3)
, a__U53(X1, X2, X3) -> U53(X1, X2, X3)
, a__U54(X1, X2, X3) -> U54(X1, X2, X3)
, a__U55(X1, X2) -> U55(X1, X2)
, a__U56(X) -> U56(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X1, X2) -> U62(X1, X2)
, a__isPLNatKind(X) -> isPLNatKind(X)
, a__U63(X) -> U63(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U73(X) -> U73(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X1, X2) -> U82(X1, X2)
, a__U83(X) -> U83(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X1, X2) -> U92(X1, X2)
, a__U93(X) -> U93(X)
, a__tail(X) -> tail(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), V1, V2) -> a__U102(a__isNaturalKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isLNatKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isLNatKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNatural(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isLNat(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__U12(a__isNaturalKind(N), N, XS)
, a__U111(tt(), V2) -> a__U112(a__isLNatKind(V2))
, a__U112(tt()) -> tt()
, a__U12(tt(), N, XS) -> a__U13(a__isLNat(XS), N, XS)
, a__U121(tt(), V2) -> a__U122(a__isLNatKind(V2))
, a__U122(tt()) -> tt()
, a__U13(tt(), N, XS) -> a__U14(a__isLNatKind(XS), N, XS)
, a__U131(tt()) -> tt()
, a__U14(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U141(tt()) -> tt()
, a__U151(tt()) -> tt()
, a__U161(tt()) -> tt()
, a__U171(tt(), V2) -> a__U172(a__isLNatKind(V2))
, a__U172(tt()) -> tt()
, a__U181(tt(), V1) -> a__U182(a__isLNatKind(V1), V1)
, a__U182(tt(), V1) -> a__U183(a__isLNat(V1))
, a__U183(tt()) -> tt()
, a__U191(tt(), V1) -> a__U192(a__isNaturalKind(V1), V1)
, a__U192(tt(), V1) -> a__U193(a__isNatural(V1))
, a__U193(tt()) -> tt()
, a__U201(tt(), V1, V2) -> a__U202(a__isNaturalKind(V1), V1, V2)
, a__U202(tt(), V1, V2) -> a__U203(a__isLNatKind(V2), V1, V2)
, a__U203(tt(), V1, V2) -> a__U204(a__isLNatKind(V2), V1, V2)
, a__U204(tt(), V1, V2) -> a__U205(a__isNatural(V1), V2)
, a__U205(tt(), V2) -> a__U206(a__isLNat(V2))
, a__U206(tt()) -> tt()
, a__U21(tt(), X, Y) -> a__U22(a__isLNatKind(X), X, Y)
, a__U211(tt()) -> tt()
, a__U22(tt(), X, Y) -> a__U23(a__isLNat(Y), X, Y)
, a__U221(tt()) -> tt()
, a__U23(tt(), X, Y) -> a__U24(a__isLNatKind(Y), X)
, a__U231(tt(), V2) -> a__U232(a__isLNatKind(V2))
, a__U232(tt()) -> tt()
, a__U24(tt(), X) -> mark(X)
, a__U241(tt(), V1, V2) -> a__U242(a__isLNatKind(V1), V1, V2)
, a__U242(tt(), V1, V2) -> a__U243(a__isLNatKind(V2), V1, V2)
, a__U243(tt(), V1, V2) -> a__U244(a__isLNatKind(V2), V1, V2)
, a__U244(tt(), V1, V2) -> a__U245(a__isLNat(V1), V2)
, a__U245(tt(), V2) -> a__U246(a__isLNat(V2))
, a__U246(tt()) -> tt()
, a__U251(tt(), V1, V2) -> a__U252(a__isNaturalKind(V1), V1, V2)
, a__U252(tt(), V1, V2) -> a__U253(a__isLNatKind(V2), V1, V2)
, a__U253(tt(), V1, V2) -> a__U254(a__isLNatKind(V2), V1, V2)
, a__U254(tt(), V1, V2) -> a__U255(a__isNatural(V1), V2)
, a__U255(tt(), V2) -> a__U256(a__isLNat(V2))
, a__U256(tt()) -> tt()
, a__U261(tt(), V2) -> a__U262(a__isLNatKind(V2))
, a__U262(tt()) -> tt()
, a__U271(tt(), V2) -> a__U272(a__isLNatKind(V2))
, a__U272(tt()) -> tt()
, a__U281(tt(), N) -> a__U282(a__isNaturalKind(N), N)
, a__U282(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U291(tt(), N, XS) -> a__U292(a__isNaturalKind(N), N, XS)
, a__U292(tt(), N, XS) -> a__U293(a__isLNat(XS), N, XS)
, a__U293(tt(), N, XS) -> a__U294(a__isLNatKind(XS), N, XS)
, a__U294(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U301(tt(), X, Y) -> a__U302(a__isLNatKind(X), Y)
, a__U302(tt(), Y) -> a__U303(a__isLNat(Y), Y)
, a__U303(tt(), Y) -> a__U304(a__isLNatKind(Y), Y)
, a__U304(tt(), Y) -> mark(Y)
, a__U31(tt(), N, XS) -> a__U32(a__isNaturalKind(N), N, XS)
, a__U311(tt(), XS) -> a__U312(a__isLNatKind(XS), XS)
, a__U312(tt(), XS) -> pair(nil(), mark(XS))
, a__U32(tt(), N, XS) -> a__U33(a__isLNat(XS), N, XS)
, a__U321(tt(), N, X, XS) -> a__U322(a__isNaturalKind(N), N, X, XS)
, a__U322(tt(), N, X, XS) -> a__U323(a__isNatural(X), N, X, XS)
, a__U323(tt(), N, X, XS) -> a__U324(a__isNaturalKind(X), N, X, XS)
, a__U324(tt(), N, X, XS) -> a__U325(a__isLNat(XS), N, X, XS)
, a__U325(tt(), N, X, XS) -> a__U326(a__isLNatKind(XS), N, X, XS)
, a__U326(tt(), N, X, XS) ->
a__U327(a__splitAt(mark(N), mark(XS)), X)
, a__U327(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U33(tt(), N, XS) -> a__U34(a__isLNatKind(XS), N)
, a__U331(tt(), N, XS) -> a__U332(a__isNaturalKind(N), XS)
, a__U332(tt(), XS) -> a__U333(a__isLNat(XS), XS)
, a__U333(tt(), XS) -> a__U334(a__isLNatKind(XS), XS)
, a__U334(tt(), XS) -> mark(XS)
, a__U34(tt(), N) -> mark(N)
, a__U341(tt(), N, XS) -> a__U342(a__isNaturalKind(N), N, XS)
, a__U342(tt(), N, XS) -> a__U343(a__isLNat(XS), N, XS)
, a__U343(tt(), N, XS) -> a__U344(a__isLNatKind(XS), N, XS)
, a__U344(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U41(tt(), V1, V2) -> a__U42(a__isNaturalKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isLNatKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isLNatKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNatural(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isLNat(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNaturalKind(V1), V1, V2)
, a__U52(tt(), V1, V2) -> a__U53(a__isLNatKind(V2), V1, V2)
, a__U53(tt(), V1, V2) -> a__U54(a__isLNatKind(V2), V1, V2)
, a__U54(tt(), V1, V2) -> a__U55(a__isNatural(V1), V2)
, a__U55(tt(), V2) -> a__U56(a__isLNat(V2))
, a__U56(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNatKind(V1), V1)
, a__U62(tt(), V1) -> a__U63(a__isPLNat(V1))
, a__U63(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNaturalKind(V1), V1)
, a__U72(tt(), V1) -> a__U73(a__isNatural(V1))
, a__U73(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNatKind(V1), V1)
, a__U82(tt(), V1) -> a__U83(a__isPLNat(V1))
, a__U83(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNatKind(V1), V1)
, a__U92(tt(), V1) -> a__U93(a__isLNat(V1))
, a__U93(tt()) -> tt()
, a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
, a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
, a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__isNaturalKind(V1), V1, V2)
, a__isLNat(cons(V1, V2)) -> a__U51(a__isNaturalKind(V1), V1, V2)
, a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1)
, a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1)
, a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1)
, a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1)
, a__isLNat(take(V1, V2)) -> a__U101(a__isNaturalKind(V1), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__U111(a__isNaturalKind(V1), V2)
, a__isLNatKind(cons(V1, V2)) -> a__U121(a__isNaturalKind(V1), V2)
, a__isLNatKind(fst(V1)) -> a__U131(a__isPLNatKind(V1))
, a__isLNatKind(natsFrom(V1)) -> a__U141(a__isNaturalKind(V1))
, a__isLNatKind(snd(V1)) -> a__U151(a__isPLNatKind(V1))
, a__isLNatKind(tail(V1)) -> a__U161(a__isLNatKind(V1))
, a__isLNatKind(take(V1, V2)) -> a__U171(a__isNaturalKind(V1), V2)
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U181(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U191(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U201(a__isNaturalKind(V1), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__U211(a__isLNatKind(V1))
, a__isNaturalKind(s(V1)) -> a__U221(a__isNaturalKind(V1))
, a__isNaturalKind(sel(V1, V2)) ->
a__U231(a__isNaturalKind(V1), V2)
, a__isPLNat(pair(V1, V2)) -> a__U241(a__isLNatKind(V1), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U251(a__isNaturalKind(V1), V1, V2)
, a__isPLNatKind(pair(V1, V2)) -> a__U261(a__isLNatKind(V1), V2)
, a__isPLNatKind(splitAt(V1, V2)) ->
a__U271(a__isNaturalKind(V1), V2)
, a__natsFrom(N) -> a__U281(a__isNatural(N), N)
, a__sel(N, XS) -> a__U291(a__isNatural(N), N, XS)
, a__snd(pair(X, Y)) -> a__U301(a__isLNat(X), X, Y)
, a__splitAt(0(), XS) -> a__U311(a__isLNat(XS), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U321(a__isNatural(N), N, X, XS)
, a__tail(cons(N, XS)) -> a__U331(a__isNatural(N), N, XS)
, a__take(N, XS) -> a__U341(a__isNatural(N), N, XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U131(X)) -> a__U131(mark(X))
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U141(X)) -> a__U141(mark(X))
, mark(U151(X)) -> a__U151(mark(X))
, mark(U161(X)) -> a__U161(mark(X))
, mark(U171(X1, X2)) -> a__U171(mark(X1), X2)
, mark(U172(X)) -> a__U172(mark(X))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U182(X1, X2)) -> a__U182(mark(X1), X2)
, mark(U183(X)) -> a__U183(mark(X))
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U192(X1, X2)) -> a__U192(mark(X1), X2)
, mark(U193(X)) -> a__U193(mark(X))
, mark(U201(X1, X2, X3)) -> a__U201(mark(X1), X2, X3)
, mark(U202(X1, X2, X3)) -> a__U202(mark(X1), X2, X3)
, mark(U203(X1, X2, X3)) -> a__U203(mark(X1), X2, X3)
, mark(U204(X1, X2, X3)) -> a__U204(mark(X1), X2, X3)
, mark(U205(X1, X2)) -> a__U205(mark(X1), X2)
, mark(U206(X)) -> a__U206(mark(X))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(U211(X)) -> a__U211(mark(X))
, mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
, mark(U221(X)) -> a__U221(mark(X))
, mark(U24(X1, X2)) -> a__U24(mark(X1), X2)
, mark(U231(X1, X2)) -> a__U231(mark(X1), X2)
, mark(U232(X)) -> a__U232(mark(X))
, mark(U241(X1, X2, X3)) -> a__U241(mark(X1), X2, X3)
, mark(U242(X1, X2, X3)) -> a__U242(mark(X1), X2, X3)
, mark(U243(X1, X2, X3)) -> a__U243(mark(X1), X2, X3)
, mark(U244(X1, X2, X3)) -> a__U244(mark(X1), X2, X3)
, mark(U245(X1, X2)) -> a__U245(mark(X1), X2)
, mark(U246(X)) -> a__U246(mark(X))
, mark(U251(X1, X2, X3)) -> a__U251(mark(X1), X2, X3)
, mark(U252(X1, X2, X3)) -> a__U252(mark(X1), X2, X3)
, mark(U253(X1, X2, X3)) -> a__U253(mark(X1), X2, X3)
, mark(U254(X1, X2, X3)) -> a__U254(mark(X1), X2, X3)
, mark(U255(X1, X2)) -> a__U255(mark(X1), X2)
, mark(U256(X)) -> a__U256(mark(X))
, mark(U261(X1, X2)) -> a__U261(mark(X1), X2)
, mark(U262(X)) -> a__U262(mark(X))
, mark(U271(X1, X2)) -> a__U271(mark(X1), X2)
, mark(U272(X)) -> a__U272(mark(X))
, mark(U281(X1, X2)) -> a__U281(mark(X1), X2)
, mark(U282(X1, X2)) -> a__U282(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U291(X1, X2, X3)) -> a__U291(mark(X1), X2, X3)
, mark(U292(X1, X2, X3)) -> a__U292(mark(X1), X2, X3)
, mark(U293(X1, X2, X3)) -> a__U293(mark(X1), X2, X3)
, mark(U294(X1, X2, X3)) -> a__U294(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U301(X1, X2, X3)) -> a__U301(mark(X1), X2, X3)
, mark(U302(X1, X2)) -> a__U302(mark(X1), X2)
, mark(U303(X1, X2)) -> a__U303(mark(X1), X2)
, mark(U304(X1, X2)) -> a__U304(mark(X1), X2)
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U311(X1, X2)) -> a__U311(mark(X1), X2)
, mark(U312(X1, X2)) -> a__U312(mark(X1), X2)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U321(X1, X2, X3, X4)) -> a__U321(mark(X1), X2, X3, X4)
, mark(U322(X1, X2, X3, X4)) -> a__U322(mark(X1), X2, X3, X4)
, mark(U323(X1, X2, X3, X4)) -> a__U323(mark(X1), X2, X3, X4)
, mark(U324(X1, X2, X3, X4)) -> a__U324(mark(X1), X2, X3, X4)
, mark(U325(X1, X2, X3, X4)) -> a__U325(mark(X1), X2, X3, X4)
, mark(U326(X1, X2, X3, X4)) -> a__U326(mark(X1), X2, X3, X4)
, mark(U327(X1, X2)) -> a__U327(mark(X1), X2)
, mark(U34(X1, X2)) -> a__U34(mark(X1), X2)
, mark(U331(X1, X2, X3)) -> a__U331(mark(X1), X2, X3)
, mark(U332(X1, X2)) -> a__U332(mark(X1), X2)
, mark(U333(X1, X2)) -> a__U333(mark(X1), X2)
, mark(U334(X1, X2)) -> a__U334(mark(X1), X2)
, mark(U341(X1, X2, X3)) -> a__U341(mark(X1), X2, X3)
, mark(U342(X1, X2, X3)) -> a__U342(mark(X1), X2, X3)
, mark(U343(X1, X2, X3)) -> a__U343(mark(X1), X2, X3)
, mark(U344(X1, X2, X3)) -> a__U344(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
, mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
, mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
, mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
, mark(U56(X)) -> a__U56(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(isPLNatKind(X)) -> a__isPLNatKind(X)
, mark(U63(X)) -> a__U63(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U73(X)) -> a__U73(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
, mark(U83(X)) -> a__U83(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X1, X2)) -> a__U92(mark(X1), X2)
, mark(U93(X)) -> a__U93(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, mark(nil()) -> nil()
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isLNatKind(X) -> isLNatKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U106(X) -> U106(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U131(X) -> U131(X)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U141(X) -> U141(X)
, a__U151(X) -> U151(X)
, a__U161(X) -> U161(X)
, a__U171(X1, X2) -> U171(X1, X2)
, a__U172(X) -> U172(X)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U182(X1, X2) -> U182(X1, X2)
, a__U183(X) -> U183(X)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U192(X1, X2) -> U192(X1, X2)
, a__U193(X) -> U193(X)
, a__U201(X1, X2, X3) -> U201(X1, X2, X3)
, a__U202(X1, X2, X3) -> U202(X1, X2, X3)
, a__U203(X1, X2, X3) -> U203(X1, X2, X3)
, a__U204(X1, X2, X3) -> U204(X1, X2, X3)
, a__U205(X1, X2) -> U205(X1, X2)
, a__U206(X) -> U206(X)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__U211(X) -> U211(X)
, a__U23(X1, X2, X3) -> U23(X1, X2, X3)
, a__U221(X) -> U221(X)
, a__U24(X1, X2) -> U24(X1, X2)
, a__U231(X1, X2) -> U231(X1, X2)
, a__U232(X) -> U232(X)
, a__U241(X1, X2, X3) -> U241(X1, X2, X3)
, a__U242(X1, X2, X3) -> U242(X1, X2, X3)
, a__U243(X1, X2, X3) -> U243(X1, X2, X3)
, a__U244(X1, X2, X3) -> U244(X1, X2, X3)
, a__U245(X1, X2) -> U245(X1, X2)
, a__U246(X) -> U246(X)
, a__U251(X1, X2, X3) -> U251(X1, X2, X3)
, a__U252(X1, X2, X3) -> U252(X1, X2, X3)
, a__U253(X1, X2, X3) -> U253(X1, X2, X3)
, a__U254(X1, X2, X3) -> U254(X1, X2, X3)
, a__U255(X1, X2) -> U255(X1, X2)
, a__U256(X) -> U256(X)
, a__U261(X1, X2) -> U261(X1, X2)
, a__U262(X) -> U262(X)
, a__U271(X1, X2) -> U271(X1, X2)
, a__U272(X) -> U272(X)
, a__U281(X1, X2) -> U281(X1, X2)
, a__U282(X1, X2) -> U282(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U291(X1, X2, X3) -> U291(X1, X2, X3)
, a__U292(X1, X2, X3) -> U292(X1, X2, X3)
, a__U293(X1, X2, X3) -> U293(X1, X2, X3)
, a__U294(X1, X2, X3) -> U294(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U301(X1, X2, X3) -> U301(X1, X2, X3)
, a__U302(X1, X2) -> U302(X1, X2)
, a__U303(X1, X2) -> U303(X1, X2)
, a__U304(X1, X2) -> U304(X1, X2)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U311(X1, X2) -> U311(X1, X2)
, a__U312(X1, X2) -> U312(X1, X2)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U321(X1, X2, X3, X4) -> U321(X1, X2, X3, X4)
, a__U322(X1, X2, X3, X4) -> U322(X1, X2, X3, X4)
, a__U323(X1, X2, X3, X4) -> U323(X1, X2, X3, X4)
, a__U324(X1, X2, X3, X4) -> U324(X1, X2, X3, X4)
, a__U325(X1, X2, X3, X4) -> U325(X1, X2, X3, X4)
, a__U326(X1, X2, X3, X4) -> U326(X1, X2, X3, X4)
, a__U327(X1, X2) -> U327(X1, X2)
, a__U34(X1, X2) -> U34(X1, X2)
, a__U331(X1, X2, X3) -> U331(X1, X2, X3)
, a__U332(X1, X2) -> U332(X1, X2)
, a__U333(X1, X2) -> U333(X1, X2)
, a__U334(X1, X2) -> U334(X1, X2)
, a__U341(X1, X2, X3) -> U341(X1, X2, X3)
, a__U342(X1, X2, X3) -> U342(X1, X2, X3)
, a__U343(X1, X2, X3) -> U343(X1, X2, X3)
, a__U344(X1, X2, X3) -> U344(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2, X3) -> U52(X1, X2, X3)
, a__U53(X1, X2, X3) -> U53(X1, X2, X3)
, a__U54(X1, X2, X3) -> U54(X1, X2, X3)
, a__U55(X1, X2) -> U55(X1, X2)
, a__U56(X) -> U56(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X1, X2) -> U62(X1, X2)
, a__isPLNatKind(X) -> isPLNatKind(X)
, a__U63(X) -> U63(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U73(X) -> U73(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X1, X2) -> U82(X1, X2)
, a__U83(X) -> U83(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X1, X2) -> U92(X1, X2)
, a__U93(X) -> U93(X)
, a__tail(X) -> tail(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), V1, V2) -> a__U102(a__isNaturalKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isLNatKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isLNatKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNatural(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isLNat(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__U12(a__isNaturalKind(N), N, XS)
, a__U111(tt(), V2) -> a__U112(a__isLNatKind(V2))
, a__U112(tt()) -> tt()
, a__U12(tt(), N, XS) -> a__U13(a__isLNat(XS), N, XS)
, a__U121(tt(), V2) -> a__U122(a__isLNatKind(V2))
, a__U122(tt()) -> tt()
, a__U13(tt(), N, XS) -> a__U14(a__isLNatKind(XS), N, XS)
, a__U131(tt()) -> tt()
, a__U14(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U141(tt()) -> tt()
, a__U151(tt()) -> tt()
, a__U161(tt()) -> tt()
, a__U171(tt(), V2) -> a__U172(a__isLNatKind(V2))
, a__U172(tt()) -> tt()
, a__U181(tt(), V1) -> a__U182(a__isLNatKind(V1), V1)
, a__U182(tt(), V1) -> a__U183(a__isLNat(V1))
, a__U183(tt()) -> tt()
, a__U191(tt(), V1) -> a__U192(a__isNaturalKind(V1), V1)
, a__U192(tt(), V1) -> a__U193(a__isNatural(V1))
, a__U193(tt()) -> tt()
, a__U201(tt(), V1, V2) -> a__U202(a__isNaturalKind(V1), V1, V2)
, a__U202(tt(), V1, V2) -> a__U203(a__isLNatKind(V2), V1, V2)
, a__U203(tt(), V1, V2) -> a__U204(a__isLNatKind(V2), V1, V2)
, a__U204(tt(), V1, V2) -> a__U205(a__isNatural(V1), V2)
, a__U205(tt(), V2) -> a__U206(a__isLNat(V2))
, a__U206(tt()) -> tt()
, a__U21(tt(), X, Y) -> a__U22(a__isLNatKind(X), X, Y)
, a__U211(tt()) -> tt()
, a__U22(tt(), X, Y) -> a__U23(a__isLNat(Y), X, Y)
, a__U221(tt()) -> tt()
, a__U23(tt(), X, Y) -> a__U24(a__isLNatKind(Y), X)
, a__U231(tt(), V2) -> a__U232(a__isLNatKind(V2))
, a__U232(tt()) -> tt()
, a__U24(tt(), X) -> mark(X)
, a__U241(tt(), V1, V2) -> a__U242(a__isLNatKind(V1), V1, V2)
, a__U242(tt(), V1, V2) -> a__U243(a__isLNatKind(V2), V1, V2)
, a__U243(tt(), V1, V2) -> a__U244(a__isLNatKind(V2), V1, V2)
, a__U244(tt(), V1, V2) -> a__U245(a__isLNat(V1), V2)
, a__U245(tt(), V2) -> a__U246(a__isLNat(V2))
, a__U246(tt()) -> tt()
, a__U251(tt(), V1, V2) -> a__U252(a__isNaturalKind(V1), V1, V2)
, a__U252(tt(), V1, V2) -> a__U253(a__isLNatKind(V2), V1, V2)
, a__U253(tt(), V1, V2) -> a__U254(a__isLNatKind(V2), V1, V2)
, a__U254(tt(), V1, V2) -> a__U255(a__isNatural(V1), V2)
, a__U255(tt(), V2) -> a__U256(a__isLNat(V2))
, a__U256(tt()) -> tt()
, a__U261(tt(), V2) -> a__U262(a__isLNatKind(V2))
, a__U262(tt()) -> tt()
, a__U271(tt(), V2) -> a__U272(a__isLNatKind(V2))
, a__U272(tt()) -> tt()
, a__U281(tt(), N) -> a__U282(a__isNaturalKind(N), N)
, a__U282(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U291(tt(), N, XS) -> a__U292(a__isNaturalKind(N), N, XS)
, a__U292(tt(), N, XS) -> a__U293(a__isLNat(XS), N, XS)
, a__U293(tt(), N, XS) -> a__U294(a__isLNatKind(XS), N, XS)
, a__U294(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U301(tt(), X, Y) -> a__U302(a__isLNatKind(X), Y)
, a__U302(tt(), Y) -> a__U303(a__isLNat(Y), Y)
, a__U303(tt(), Y) -> a__U304(a__isLNatKind(Y), Y)
, a__U304(tt(), Y) -> mark(Y)
, a__U31(tt(), N, XS) -> a__U32(a__isNaturalKind(N), N, XS)
, a__U311(tt(), XS) -> a__U312(a__isLNatKind(XS), XS)
, a__U312(tt(), XS) -> pair(nil(), mark(XS))
, a__U32(tt(), N, XS) -> a__U33(a__isLNat(XS), N, XS)
, a__U321(tt(), N, X, XS) -> a__U322(a__isNaturalKind(N), N, X, XS)
, a__U322(tt(), N, X, XS) -> a__U323(a__isNatural(X), N, X, XS)
, a__U323(tt(), N, X, XS) -> a__U324(a__isNaturalKind(X), N, X, XS)
, a__U324(tt(), N, X, XS) -> a__U325(a__isLNat(XS), N, X, XS)
, a__U325(tt(), N, X, XS) -> a__U326(a__isLNatKind(XS), N, X, XS)
, a__U326(tt(), N, X, XS) ->
a__U327(a__splitAt(mark(N), mark(XS)), X)
, a__U327(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U33(tt(), N, XS) -> a__U34(a__isLNatKind(XS), N)
, a__U331(tt(), N, XS) -> a__U332(a__isNaturalKind(N), XS)
, a__U332(tt(), XS) -> a__U333(a__isLNat(XS), XS)
, a__U333(tt(), XS) -> a__U334(a__isLNatKind(XS), XS)
, a__U334(tt(), XS) -> mark(XS)
, a__U34(tt(), N) -> mark(N)
, a__U341(tt(), N, XS) -> a__U342(a__isNaturalKind(N), N, XS)
, a__U342(tt(), N, XS) -> a__U343(a__isLNat(XS), N, XS)
, a__U343(tt(), N, XS) -> a__U344(a__isLNatKind(XS), N, XS)
, a__U344(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U41(tt(), V1, V2) -> a__U42(a__isNaturalKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isLNatKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isLNatKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNatural(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isLNat(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNaturalKind(V1), V1, V2)
, a__U52(tt(), V1, V2) -> a__U53(a__isLNatKind(V2), V1, V2)
, a__U53(tt(), V1, V2) -> a__U54(a__isLNatKind(V2), V1, V2)
, a__U54(tt(), V1, V2) -> a__U55(a__isNatural(V1), V2)
, a__U55(tt(), V2) -> a__U56(a__isLNat(V2))
, a__U56(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNatKind(V1), V1)
, a__U62(tt(), V1) -> a__U63(a__isPLNat(V1))
, a__U63(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNaturalKind(V1), V1)
, a__U72(tt(), V1) -> a__U73(a__isNatural(V1))
, a__U73(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNatKind(V1), V1)
, a__U82(tt(), V1) -> a__U83(a__isPLNat(V1))
, a__U83(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNatKind(V1), V1)
, a__U92(tt(), V1) -> a__U93(a__isLNat(V1))
, a__U93(tt()) -> tt()
, a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
, a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
, a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__isNaturalKind(V1), V1, V2)
, a__isLNat(cons(V1, V2)) -> a__U51(a__isNaturalKind(V1), V1, V2)
, a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1)
, a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1)
, a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1)
, a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1)
, a__isLNat(take(V1, V2)) -> a__U101(a__isNaturalKind(V1), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__U111(a__isNaturalKind(V1), V2)
, a__isLNatKind(cons(V1, V2)) -> a__U121(a__isNaturalKind(V1), V2)
, a__isLNatKind(fst(V1)) -> a__U131(a__isPLNatKind(V1))
, a__isLNatKind(natsFrom(V1)) -> a__U141(a__isNaturalKind(V1))
, a__isLNatKind(snd(V1)) -> a__U151(a__isPLNatKind(V1))
, a__isLNatKind(tail(V1)) -> a__U161(a__isLNatKind(V1))
, a__isLNatKind(take(V1, V2)) -> a__U171(a__isNaturalKind(V1), V2)
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U181(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U191(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U201(a__isNaturalKind(V1), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__U211(a__isLNatKind(V1))
, a__isNaturalKind(s(V1)) -> a__U221(a__isNaturalKind(V1))
, a__isNaturalKind(sel(V1, V2)) ->
a__U231(a__isNaturalKind(V1), V2)
, a__isPLNat(pair(V1, V2)) -> a__U241(a__isLNatKind(V1), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U251(a__isNaturalKind(V1), V1, V2)
, a__isPLNatKind(pair(V1, V2)) -> a__U261(a__isLNatKind(V1), V2)
, a__isPLNatKind(splitAt(V1, V2)) ->
a__U271(a__isNaturalKind(V1), V2)
, a__natsFrom(N) -> a__U281(a__isNatural(N), N)
, a__sel(N, XS) -> a__U291(a__isNatural(N), N, XS)
, a__snd(pair(X, Y)) -> a__U301(a__isLNat(X), X, Y)
, a__splitAt(0(), XS) -> a__U311(a__isLNat(XS), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U321(a__isNatural(N), N, X, XS)
, a__tail(cons(N, XS)) -> a__U331(a__isNatural(N), N, XS)
, a__take(N, XS) -> a__U341(a__isNatural(N), N, XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U131(X)) -> a__U131(mark(X))
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U141(X)) -> a__U141(mark(X))
, mark(U151(X)) -> a__U151(mark(X))
, mark(U161(X)) -> a__U161(mark(X))
, mark(U171(X1, X2)) -> a__U171(mark(X1), X2)
, mark(U172(X)) -> a__U172(mark(X))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U182(X1, X2)) -> a__U182(mark(X1), X2)
, mark(U183(X)) -> a__U183(mark(X))
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U192(X1, X2)) -> a__U192(mark(X1), X2)
, mark(U193(X)) -> a__U193(mark(X))
, mark(U201(X1, X2, X3)) -> a__U201(mark(X1), X2, X3)
, mark(U202(X1, X2, X3)) -> a__U202(mark(X1), X2, X3)
, mark(U203(X1, X2, X3)) -> a__U203(mark(X1), X2, X3)
, mark(U204(X1, X2, X3)) -> a__U204(mark(X1), X2, X3)
, mark(U205(X1, X2)) -> a__U205(mark(X1), X2)
, mark(U206(X)) -> a__U206(mark(X))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(U211(X)) -> a__U211(mark(X))
, mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
, mark(U221(X)) -> a__U221(mark(X))
, mark(U24(X1, X2)) -> a__U24(mark(X1), X2)
, mark(U231(X1, X2)) -> a__U231(mark(X1), X2)
, mark(U232(X)) -> a__U232(mark(X))
, mark(U241(X1, X2, X3)) -> a__U241(mark(X1), X2, X3)
, mark(U242(X1, X2, X3)) -> a__U242(mark(X1), X2, X3)
, mark(U243(X1, X2, X3)) -> a__U243(mark(X1), X2, X3)
, mark(U244(X1, X2, X3)) -> a__U244(mark(X1), X2, X3)
, mark(U245(X1, X2)) -> a__U245(mark(X1), X2)
, mark(U246(X)) -> a__U246(mark(X))
, mark(U251(X1, X2, X3)) -> a__U251(mark(X1), X2, X3)
, mark(U252(X1, X2, X3)) -> a__U252(mark(X1), X2, X3)
, mark(U253(X1, X2, X3)) -> a__U253(mark(X1), X2, X3)
, mark(U254(X1, X2, X3)) -> a__U254(mark(X1), X2, X3)
, mark(U255(X1, X2)) -> a__U255(mark(X1), X2)
, mark(U256(X)) -> a__U256(mark(X))
, mark(U261(X1, X2)) -> a__U261(mark(X1), X2)
, mark(U262(X)) -> a__U262(mark(X))
, mark(U271(X1, X2)) -> a__U271(mark(X1), X2)
, mark(U272(X)) -> a__U272(mark(X))
, mark(U281(X1, X2)) -> a__U281(mark(X1), X2)
, mark(U282(X1, X2)) -> a__U282(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U291(X1, X2, X3)) -> a__U291(mark(X1), X2, X3)
, mark(U292(X1, X2, X3)) -> a__U292(mark(X1), X2, X3)
, mark(U293(X1, X2, X3)) -> a__U293(mark(X1), X2, X3)
, mark(U294(X1, X2, X3)) -> a__U294(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U301(X1, X2, X3)) -> a__U301(mark(X1), X2, X3)
, mark(U302(X1, X2)) -> a__U302(mark(X1), X2)
, mark(U303(X1, X2)) -> a__U303(mark(X1), X2)
, mark(U304(X1, X2)) -> a__U304(mark(X1), X2)
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U311(X1, X2)) -> a__U311(mark(X1), X2)
, mark(U312(X1, X2)) -> a__U312(mark(X1), X2)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U321(X1, X2, X3, X4)) -> a__U321(mark(X1), X2, X3, X4)
, mark(U322(X1, X2, X3, X4)) -> a__U322(mark(X1), X2, X3, X4)
, mark(U323(X1, X2, X3, X4)) -> a__U323(mark(X1), X2, X3, X4)
, mark(U324(X1, X2, X3, X4)) -> a__U324(mark(X1), X2, X3, X4)
, mark(U325(X1, X2, X3, X4)) -> a__U325(mark(X1), X2, X3, X4)
, mark(U326(X1, X2, X3, X4)) -> a__U326(mark(X1), X2, X3, X4)
, mark(U327(X1, X2)) -> a__U327(mark(X1), X2)
, mark(U34(X1, X2)) -> a__U34(mark(X1), X2)
, mark(U331(X1, X2, X3)) -> a__U331(mark(X1), X2, X3)
, mark(U332(X1, X2)) -> a__U332(mark(X1), X2)
, mark(U333(X1, X2)) -> a__U333(mark(X1), X2)
, mark(U334(X1, X2)) -> a__U334(mark(X1), X2)
, mark(U341(X1, X2, X3)) -> a__U341(mark(X1), X2, X3)
, mark(U342(X1, X2, X3)) -> a__U342(mark(X1), X2, X3)
, mark(U343(X1, X2, X3)) -> a__U343(mark(X1), X2, X3)
, mark(U344(X1, X2, X3)) -> a__U344(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
, mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
, mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
, mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
, mark(U56(X)) -> a__U56(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(isPLNatKind(X)) -> a__isPLNatKind(X)
, mark(U63(X)) -> a__U63(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U73(X)) -> a__U73(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
, mark(U83(X)) -> a__U83(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X1, X2)) -> a__U92(mark(X1), X2)
, mark(U93(X)) -> a__U93(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, mark(nil()) -> nil()
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isLNatKind(X) -> isLNatKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U106(X) -> U106(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U131(X) -> U131(X)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U141(X) -> U141(X)
, a__U151(X) -> U151(X)
, a__U161(X) -> U161(X)
, a__U171(X1, X2) -> U171(X1, X2)
, a__U172(X) -> U172(X)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U182(X1, X2) -> U182(X1, X2)
, a__U183(X) -> U183(X)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U192(X1, X2) -> U192(X1, X2)
, a__U193(X) -> U193(X)
, a__U201(X1, X2, X3) -> U201(X1, X2, X3)
, a__U202(X1, X2, X3) -> U202(X1, X2, X3)
, a__U203(X1, X2, X3) -> U203(X1, X2, X3)
, a__U204(X1, X2, X3) -> U204(X1, X2, X3)
, a__U205(X1, X2) -> U205(X1, X2)
, a__U206(X) -> U206(X)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__U211(X) -> U211(X)
, a__U23(X1, X2, X3) -> U23(X1, X2, X3)
, a__U221(X) -> U221(X)
, a__U24(X1, X2) -> U24(X1, X2)
, a__U231(X1, X2) -> U231(X1, X2)
, a__U232(X) -> U232(X)
, a__U241(X1, X2, X3) -> U241(X1, X2, X3)
, a__U242(X1, X2, X3) -> U242(X1, X2, X3)
, a__U243(X1, X2, X3) -> U243(X1, X2, X3)
, a__U244(X1, X2, X3) -> U244(X1, X2, X3)
, a__U245(X1, X2) -> U245(X1, X2)
, a__U246(X) -> U246(X)
, a__U251(X1, X2, X3) -> U251(X1, X2, X3)
, a__U252(X1, X2, X3) -> U252(X1, X2, X3)
, a__U253(X1, X2, X3) -> U253(X1, X2, X3)
, a__U254(X1, X2, X3) -> U254(X1, X2, X3)
, a__U255(X1, X2) -> U255(X1, X2)
, a__U256(X) -> U256(X)
, a__U261(X1, X2) -> U261(X1, X2)
, a__U262(X) -> U262(X)
, a__U271(X1, X2) -> U271(X1, X2)
, a__U272(X) -> U272(X)
, a__U281(X1, X2) -> U281(X1, X2)
, a__U282(X1, X2) -> U282(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U291(X1, X2, X3) -> U291(X1, X2, X3)
, a__U292(X1, X2, X3) -> U292(X1, X2, X3)
, a__U293(X1, X2, X3) -> U293(X1, X2, X3)
, a__U294(X1, X2, X3) -> U294(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U301(X1, X2, X3) -> U301(X1, X2, X3)
, a__U302(X1, X2) -> U302(X1, X2)
, a__U303(X1, X2) -> U303(X1, X2)
, a__U304(X1, X2) -> U304(X1, X2)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U311(X1, X2) -> U311(X1, X2)
, a__U312(X1, X2) -> U312(X1, X2)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U321(X1, X2, X3, X4) -> U321(X1, X2, X3, X4)
, a__U322(X1, X2, X3, X4) -> U322(X1, X2, X3, X4)
, a__U323(X1, X2, X3, X4) -> U323(X1, X2, X3, X4)
, a__U324(X1, X2, X3, X4) -> U324(X1, X2, X3, X4)
, a__U325(X1, X2, X3, X4) -> U325(X1, X2, X3, X4)
, a__U326(X1, X2, X3, X4) -> U326(X1, X2, X3, X4)
, a__U327(X1, X2) -> U327(X1, X2)
, a__U34(X1, X2) -> U34(X1, X2)
, a__U331(X1, X2, X3) -> U331(X1, X2, X3)
, a__U332(X1, X2) -> U332(X1, X2)
, a__U333(X1, X2) -> U333(X1, X2)
, a__U334(X1, X2) -> U334(X1, X2)
, a__U341(X1, X2, X3) -> U341(X1, X2, X3)
, a__U342(X1, X2, X3) -> U342(X1, X2, X3)
, a__U343(X1, X2, X3) -> U343(X1, X2, X3)
, a__U344(X1, X2, X3) -> U344(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2, X3) -> U52(X1, X2, X3)
, a__U53(X1, X2, X3) -> U53(X1, X2, X3)
, a__U54(X1, X2, X3) -> U54(X1, X2, X3)
, a__U55(X1, X2) -> U55(X1, X2)
, a__U56(X) -> U56(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X1, X2) -> U62(X1, X2)
, a__isPLNatKind(X) -> isPLNatKind(X)
, a__U63(X) -> U63(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U73(X) -> U73(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X1, X2) -> U82(X1, X2)
, a__U83(X) -> U83(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X1, X2) -> U92(X1, X2)
, a__U93(X) -> U93(X)
, a__tail(X) -> tail(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..
Small POP* (PS)
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), V1, V2) -> a__U102(a__isNaturalKind(V1), V1, V2)
, a__U102(tt(), V1, V2) -> a__U103(a__isLNatKind(V2), V1, V2)
, a__U103(tt(), V1, V2) -> a__U104(a__isLNatKind(V2), V1, V2)
, a__U104(tt(), V1, V2) -> a__U105(a__isNatural(V1), V2)
, a__U105(tt(), V2) -> a__U106(a__isLNat(V2))
, a__U106(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__U12(a__isNaturalKind(N), N, XS)
, a__U111(tt(), V2) -> a__U112(a__isLNatKind(V2))
, a__U112(tt()) -> tt()
, a__U12(tt(), N, XS) -> a__U13(a__isLNat(XS), N, XS)
, a__U121(tt(), V2) -> a__U122(a__isLNatKind(V2))
, a__U122(tt()) -> tt()
, a__U13(tt(), N, XS) -> a__U14(a__isLNatKind(XS), N, XS)
, a__U131(tt()) -> tt()
, a__U14(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U141(tt()) -> tt()
, a__U151(tt()) -> tt()
, a__U161(tt()) -> tt()
, a__U171(tt(), V2) -> a__U172(a__isLNatKind(V2))
, a__U172(tt()) -> tt()
, a__U181(tt(), V1) -> a__U182(a__isLNatKind(V1), V1)
, a__U182(tt(), V1) -> a__U183(a__isLNat(V1))
, a__U183(tt()) -> tt()
, a__U191(tt(), V1) -> a__U192(a__isNaturalKind(V1), V1)
, a__U192(tt(), V1) -> a__U193(a__isNatural(V1))
, a__U193(tt()) -> tt()
, a__U201(tt(), V1, V2) -> a__U202(a__isNaturalKind(V1), V1, V2)
, a__U202(tt(), V1, V2) -> a__U203(a__isLNatKind(V2), V1, V2)
, a__U203(tt(), V1, V2) -> a__U204(a__isLNatKind(V2), V1, V2)
, a__U204(tt(), V1, V2) -> a__U205(a__isNatural(V1), V2)
, a__U205(tt(), V2) -> a__U206(a__isLNat(V2))
, a__U206(tt()) -> tt()
, a__U21(tt(), X, Y) -> a__U22(a__isLNatKind(X), X, Y)
, a__U211(tt()) -> tt()
, a__U22(tt(), X, Y) -> a__U23(a__isLNat(Y), X, Y)
, a__U221(tt()) -> tt()
, a__U23(tt(), X, Y) -> a__U24(a__isLNatKind(Y), X)
, a__U231(tt(), V2) -> a__U232(a__isLNatKind(V2))
, a__U232(tt()) -> tt()
, a__U24(tt(), X) -> mark(X)
, a__U241(tt(), V1, V2) -> a__U242(a__isLNatKind(V1), V1, V2)
, a__U242(tt(), V1, V2) -> a__U243(a__isLNatKind(V2), V1, V2)
, a__U243(tt(), V1, V2) -> a__U244(a__isLNatKind(V2), V1, V2)
, a__U244(tt(), V1, V2) -> a__U245(a__isLNat(V1), V2)
, a__U245(tt(), V2) -> a__U246(a__isLNat(V2))
, a__U246(tt()) -> tt()
, a__U251(tt(), V1, V2) -> a__U252(a__isNaturalKind(V1), V1, V2)
, a__U252(tt(), V1, V2) -> a__U253(a__isLNatKind(V2), V1, V2)
, a__U253(tt(), V1, V2) -> a__U254(a__isLNatKind(V2), V1, V2)
, a__U254(tt(), V1, V2) -> a__U255(a__isNatural(V1), V2)
, a__U255(tt(), V2) -> a__U256(a__isLNat(V2))
, a__U256(tt()) -> tt()
, a__U261(tt(), V2) -> a__U262(a__isLNatKind(V2))
, a__U262(tt()) -> tt()
, a__U271(tt(), V2) -> a__U272(a__isLNatKind(V2))
, a__U272(tt()) -> tt()
, a__U281(tt(), N) -> a__U282(a__isNaturalKind(N), N)
, a__U282(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U291(tt(), N, XS) -> a__U292(a__isNaturalKind(N), N, XS)
, a__U292(tt(), N, XS) -> a__U293(a__isLNat(XS), N, XS)
, a__U293(tt(), N, XS) -> a__U294(a__isLNatKind(XS), N, XS)
, a__U294(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U301(tt(), X, Y) -> a__U302(a__isLNatKind(X), Y)
, a__U302(tt(), Y) -> a__U303(a__isLNat(Y), Y)
, a__U303(tt(), Y) -> a__U304(a__isLNatKind(Y), Y)
, a__U304(tt(), Y) -> mark(Y)
, a__U31(tt(), N, XS) -> a__U32(a__isNaturalKind(N), N, XS)
, a__U311(tt(), XS) -> a__U312(a__isLNatKind(XS), XS)
, a__U312(tt(), XS) -> pair(nil(), mark(XS))
, a__U32(tt(), N, XS) -> a__U33(a__isLNat(XS), N, XS)
, a__U321(tt(), N, X, XS) -> a__U322(a__isNaturalKind(N), N, X, XS)
, a__U322(tt(), N, X, XS) -> a__U323(a__isNatural(X), N, X, XS)
, a__U323(tt(), N, X, XS) -> a__U324(a__isNaturalKind(X), N, X, XS)
, a__U324(tt(), N, X, XS) -> a__U325(a__isLNat(XS), N, X, XS)
, a__U325(tt(), N, X, XS) -> a__U326(a__isLNatKind(XS), N, X, XS)
, a__U326(tt(), N, X, XS) ->
a__U327(a__splitAt(mark(N), mark(XS)), X)
, a__U327(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U33(tt(), N, XS) -> a__U34(a__isLNatKind(XS), N)
, a__U331(tt(), N, XS) -> a__U332(a__isNaturalKind(N), XS)
, a__U332(tt(), XS) -> a__U333(a__isLNat(XS), XS)
, a__U333(tt(), XS) -> a__U334(a__isLNatKind(XS), XS)
, a__U334(tt(), XS) -> mark(XS)
, a__U34(tt(), N) -> mark(N)
, a__U341(tt(), N, XS) -> a__U342(a__isNaturalKind(N), N, XS)
, a__U342(tt(), N, XS) -> a__U343(a__isLNat(XS), N, XS)
, a__U343(tt(), N, XS) -> a__U344(a__isLNatKind(XS), N, XS)
, a__U344(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U41(tt(), V1, V2) -> a__U42(a__isNaturalKind(V1), V1, V2)
, a__U42(tt(), V1, V2) -> a__U43(a__isLNatKind(V2), V1, V2)
, a__U43(tt(), V1, V2) -> a__U44(a__isLNatKind(V2), V1, V2)
, a__U44(tt(), V1, V2) -> a__U45(a__isNatural(V1), V2)
, a__U45(tt(), V2) -> a__U46(a__isLNat(V2))
, a__U46(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNaturalKind(V1), V1, V2)
, a__U52(tt(), V1, V2) -> a__U53(a__isLNatKind(V2), V1, V2)
, a__U53(tt(), V1, V2) -> a__U54(a__isLNatKind(V2), V1, V2)
, a__U54(tt(), V1, V2) -> a__U55(a__isNatural(V1), V2)
, a__U55(tt(), V2) -> a__U56(a__isLNat(V2))
, a__U56(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNatKind(V1), V1)
, a__U62(tt(), V1) -> a__U63(a__isPLNat(V1))
, a__U63(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNaturalKind(V1), V1)
, a__U72(tt(), V1) -> a__U73(a__isNatural(V1))
, a__U73(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNatKind(V1), V1)
, a__U82(tt(), V1) -> a__U83(a__isPLNat(V1))
, a__U83(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNatKind(V1), V1)
, a__U92(tt(), V1) -> a__U93(a__isLNat(V1))
, a__U93(tt()) -> tt()
, a__afterNth(N, XS) -> a__U11(a__isNatural(N), N, XS)
, a__fst(pair(X, Y)) -> a__U21(a__isLNat(X), X, Y)
, a__head(cons(N, XS)) -> a__U31(a__isNatural(N), N, XS)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__isNaturalKind(V1), V1, V2)
, a__isLNat(cons(V1, V2)) -> a__U51(a__isNaturalKind(V1), V1, V2)
, a__isLNat(fst(V1)) -> a__U61(a__isPLNatKind(V1), V1)
, a__isLNat(natsFrom(V1)) -> a__U71(a__isNaturalKind(V1), V1)
, a__isLNat(snd(V1)) -> a__U81(a__isPLNatKind(V1), V1)
, a__isLNat(tail(V1)) -> a__U91(a__isLNatKind(V1), V1)
, a__isLNat(take(V1, V2)) -> a__U101(a__isNaturalKind(V1), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__U111(a__isNaturalKind(V1), V2)
, a__isLNatKind(cons(V1, V2)) -> a__U121(a__isNaturalKind(V1), V2)
, a__isLNatKind(fst(V1)) -> a__U131(a__isPLNatKind(V1))
, a__isLNatKind(natsFrom(V1)) -> a__U141(a__isNaturalKind(V1))
, a__isLNatKind(snd(V1)) -> a__U151(a__isPLNatKind(V1))
, a__isLNatKind(tail(V1)) -> a__U161(a__isLNatKind(V1))
, a__isLNatKind(take(V1, V2)) -> a__U171(a__isNaturalKind(V1), V2)
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U181(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U191(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U201(a__isNaturalKind(V1), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__U211(a__isLNatKind(V1))
, a__isNaturalKind(s(V1)) -> a__U221(a__isNaturalKind(V1))
, a__isNaturalKind(sel(V1, V2)) ->
a__U231(a__isNaturalKind(V1), V2)
, a__isPLNat(pair(V1, V2)) -> a__U241(a__isLNatKind(V1), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U251(a__isNaturalKind(V1), V1, V2)
, a__isPLNatKind(pair(V1, V2)) -> a__U261(a__isLNatKind(V1), V2)
, a__isPLNatKind(splitAt(V1, V2)) ->
a__U271(a__isNaturalKind(V1), V2)
, a__natsFrom(N) -> a__U281(a__isNatural(N), N)
, a__sel(N, XS) -> a__U291(a__isNatural(N), N, XS)
, a__snd(pair(X, Y)) -> a__U301(a__isLNat(X), X, Y)
, a__splitAt(0(), XS) -> a__U311(a__isLNat(XS), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U321(a__isNatural(N), N, X, XS)
, a__tail(cons(N, XS)) -> a__U331(a__isNatural(N), N, XS)
, a__take(N, XS) -> a__U341(a__isNatural(N), N, XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2, X3)) -> a__U102(mark(X1), X2, X3)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(U103(X1, X2, X3)) -> a__U103(mark(X1), X2, X3)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(U104(X1, X2, X3)) -> a__U104(mark(X1), X2, X3)
, mark(U105(X1, X2)) -> a__U105(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U106(X)) -> a__U106(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U13(X1, X2, X3)) -> a__U13(mark(X1), X2, X3)
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U14(X1, X2, X3)) -> a__U14(mark(X1), X2, X3)
, mark(U131(X)) -> a__U131(mark(X))
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U141(X)) -> a__U141(mark(X))
, mark(U151(X)) -> a__U151(mark(X))
, mark(U161(X)) -> a__U161(mark(X))
, mark(U171(X1, X2)) -> a__U171(mark(X1), X2)
, mark(U172(X)) -> a__U172(mark(X))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U182(X1, X2)) -> a__U182(mark(X1), X2)
, mark(U183(X)) -> a__U183(mark(X))
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U192(X1, X2)) -> a__U192(mark(X1), X2)
, mark(U193(X)) -> a__U193(mark(X))
, mark(U201(X1, X2, X3)) -> a__U201(mark(X1), X2, X3)
, mark(U202(X1, X2, X3)) -> a__U202(mark(X1), X2, X3)
, mark(U203(X1, X2, X3)) -> a__U203(mark(X1), X2, X3)
, mark(U204(X1, X2, X3)) -> a__U204(mark(X1), X2, X3)
, mark(U205(X1, X2)) -> a__U205(mark(X1), X2)
, mark(U206(X)) -> a__U206(mark(X))
, mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
, mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
, mark(U211(X)) -> a__U211(mark(X))
, mark(U23(X1, X2, X3)) -> a__U23(mark(X1), X2, X3)
, mark(U221(X)) -> a__U221(mark(X))
, mark(U24(X1, X2)) -> a__U24(mark(X1), X2)
, mark(U231(X1, X2)) -> a__U231(mark(X1), X2)
, mark(U232(X)) -> a__U232(mark(X))
, mark(U241(X1, X2, X3)) -> a__U241(mark(X1), X2, X3)
, mark(U242(X1, X2, X3)) -> a__U242(mark(X1), X2, X3)
, mark(U243(X1, X2, X3)) -> a__U243(mark(X1), X2, X3)
, mark(U244(X1, X2, X3)) -> a__U244(mark(X1), X2, X3)
, mark(U245(X1, X2)) -> a__U245(mark(X1), X2)
, mark(U246(X)) -> a__U246(mark(X))
, mark(U251(X1, X2, X3)) -> a__U251(mark(X1), X2, X3)
, mark(U252(X1, X2, X3)) -> a__U252(mark(X1), X2, X3)
, mark(U253(X1, X2, X3)) -> a__U253(mark(X1), X2, X3)
, mark(U254(X1, X2, X3)) -> a__U254(mark(X1), X2, X3)
, mark(U255(X1, X2)) -> a__U255(mark(X1), X2)
, mark(U256(X)) -> a__U256(mark(X))
, mark(U261(X1, X2)) -> a__U261(mark(X1), X2)
, mark(U262(X)) -> a__U262(mark(X))
, mark(U271(X1, X2)) -> a__U271(mark(X1), X2)
, mark(U272(X)) -> a__U272(mark(X))
, mark(U281(X1, X2)) -> a__U281(mark(X1), X2)
, mark(U282(X1, X2)) -> a__U282(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U291(X1, X2, X3)) -> a__U291(mark(X1), X2, X3)
, mark(U292(X1, X2, X3)) -> a__U292(mark(X1), X2, X3)
, mark(U293(X1, X2, X3)) -> a__U293(mark(X1), X2, X3)
, mark(U294(X1, X2, X3)) -> a__U294(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U301(X1, X2, X3)) -> a__U301(mark(X1), X2, X3)
, mark(U302(X1, X2)) -> a__U302(mark(X1), X2)
, mark(U303(X1, X2)) -> a__U303(mark(X1), X2)
, mark(U304(X1, X2)) -> a__U304(mark(X1), X2)
, mark(U31(X1, X2, X3)) -> a__U31(mark(X1), X2, X3)
, mark(U32(X1, X2, X3)) -> a__U32(mark(X1), X2, X3)
, mark(U311(X1, X2)) -> a__U311(mark(X1), X2)
, mark(U312(X1, X2)) -> a__U312(mark(X1), X2)
, mark(U33(X1, X2, X3)) -> a__U33(mark(X1), X2, X3)
, mark(U321(X1, X2, X3, X4)) -> a__U321(mark(X1), X2, X3, X4)
, mark(U322(X1, X2, X3, X4)) -> a__U322(mark(X1), X2, X3, X4)
, mark(U323(X1, X2, X3, X4)) -> a__U323(mark(X1), X2, X3, X4)
, mark(U324(X1, X2, X3, X4)) -> a__U324(mark(X1), X2, X3, X4)
, mark(U325(X1, X2, X3, X4)) -> a__U325(mark(X1), X2, X3, X4)
, mark(U326(X1, X2, X3, X4)) -> a__U326(mark(X1), X2, X3, X4)
, mark(U327(X1, X2)) -> a__U327(mark(X1), X2)
, mark(U34(X1, X2)) -> a__U34(mark(X1), X2)
, mark(U331(X1, X2, X3)) -> a__U331(mark(X1), X2, X3)
, mark(U332(X1, X2)) -> a__U332(mark(X1), X2)
, mark(U333(X1, X2)) -> a__U333(mark(X1), X2)
, mark(U334(X1, X2)) -> a__U334(mark(X1), X2)
, mark(U341(X1, X2, X3)) -> a__U341(mark(X1), X2, X3)
, mark(U342(X1, X2, X3)) -> a__U342(mark(X1), X2, X3)
, mark(U343(X1, X2, X3)) -> a__U343(mark(X1), X2, X3)
, mark(U344(X1, X2, X3)) -> a__U344(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
, mark(U43(X1, X2, X3)) -> a__U43(mark(X1), X2, X3)
, mark(U44(X1, X2, X3)) -> a__U44(mark(X1), X2, X3)
, mark(U45(X1, X2)) -> a__U45(mark(X1), X2)
, mark(U46(X)) -> a__U46(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3)
, mark(U53(X1, X2, X3)) -> a__U53(mark(X1), X2, X3)
, mark(U54(X1, X2, X3)) -> a__U54(mark(X1), X2, X3)
, mark(U55(X1, X2)) -> a__U55(mark(X1), X2)
, mark(U56(X)) -> a__U56(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X1, X2)) -> a__U62(mark(X1), X2)
, mark(isPLNatKind(X)) -> a__isPLNatKind(X)
, mark(U63(X)) -> a__U63(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X1, X2)) -> a__U72(mark(X1), X2)
, mark(U73(X)) -> a__U73(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X1, X2)) -> a__U82(mark(X1), X2)
, mark(U83(X)) -> a__U83(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X1, X2)) -> a__U92(mark(X1), X2)
, mark(U93(X)) -> a__U93(mark(X))
, mark(tail(X)) -> a__tail(mark(X))
, mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
, mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
, mark(tt()) -> tt()
, mark(cons(X1, X2)) -> cons(mark(X1), X2)
, mark(s(X)) -> s(mark(X))
, mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
, mark(nil()) -> nil()
, mark(0()) -> 0()
, a__U101(X1, X2, X3) -> U101(X1, X2, X3)
, a__U102(X1, X2, X3) -> U102(X1, X2, X3)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__U103(X1, X2, X3) -> U103(X1, X2, X3)
, a__isLNatKind(X) -> isLNatKind(X)
, a__U104(X1, X2, X3) -> U104(X1, X2, X3)
, a__U105(X1, X2) -> U105(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U106(X) -> U106(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__U12(X1, X2, X3) -> U12(X1, X2, X3)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U13(X1, X2, X3) -> U13(X1, X2, X3)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U14(X1, X2, X3) -> U14(X1, X2, X3)
, a__U131(X) -> U131(X)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U141(X) -> U141(X)
, a__U151(X) -> U151(X)
, a__U161(X) -> U161(X)
, a__U171(X1, X2) -> U171(X1, X2)
, a__U172(X) -> U172(X)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U182(X1, X2) -> U182(X1, X2)
, a__U183(X) -> U183(X)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U192(X1, X2) -> U192(X1, X2)
, a__U193(X) -> U193(X)
, a__U201(X1, X2, X3) -> U201(X1, X2, X3)
, a__U202(X1, X2, X3) -> U202(X1, X2, X3)
, a__U203(X1, X2, X3) -> U203(X1, X2, X3)
, a__U204(X1, X2, X3) -> U204(X1, X2, X3)
, a__U205(X1, X2) -> U205(X1, X2)
, a__U206(X) -> U206(X)
, a__U21(X1, X2, X3) -> U21(X1, X2, X3)
, a__U22(X1, X2, X3) -> U22(X1, X2, X3)
, a__U211(X) -> U211(X)
, a__U23(X1, X2, X3) -> U23(X1, X2, X3)
, a__U221(X) -> U221(X)
, a__U24(X1, X2) -> U24(X1, X2)
, a__U231(X1, X2) -> U231(X1, X2)
, a__U232(X) -> U232(X)
, a__U241(X1, X2, X3) -> U241(X1, X2, X3)
, a__U242(X1, X2, X3) -> U242(X1, X2, X3)
, a__U243(X1, X2, X3) -> U243(X1, X2, X3)
, a__U244(X1, X2, X3) -> U244(X1, X2, X3)
, a__U245(X1, X2) -> U245(X1, X2)
, a__U246(X) -> U246(X)
, a__U251(X1, X2, X3) -> U251(X1, X2, X3)
, a__U252(X1, X2, X3) -> U252(X1, X2, X3)
, a__U253(X1, X2, X3) -> U253(X1, X2, X3)
, a__U254(X1, X2, X3) -> U254(X1, X2, X3)
, a__U255(X1, X2) -> U255(X1, X2)
, a__U256(X) -> U256(X)
, a__U261(X1, X2) -> U261(X1, X2)
, a__U262(X) -> U262(X)
, a__U271(X1, X2) -> U271(X1, X2)
, a__U272(X) -> U272(X)
, a__U281(X1, X2) -> U281(X1, X2)
, a__U282(X1, X2) -> U282(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U291(X1, X2, X3) -> U291(X1, X2, X3)
, a__U292(X1, X2, X3) -> U292(X1, X2, X3)
, a__U293(X1, X2, X3) -> U293(X1, X2, X3)
, a__U294(X1, X2, X3) -> U294(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U301(X1, X2, X3) -> U301(X1, X2, X3)
, a__U302(X1, X2) -> U302(X1, X2)
, a__U303(X1, X2) -> U303(X1, X2)
, a__U304(X1, X2) -> U304(X1, X2)
, a__U31(X1, X2, X3) -> U31(X1, X2, X3)
, a__U32(X1, X2, X3) -> U32(X1, X2, X3)
, a__U311(X1, X2) -> U311(X1, X2)
, a__U312(X1, X2) -> U312(X1, X2)
, a__U33(X1, X2, X3) -> U33(X1, X2, X3)
, a__U321(X1, X2, X3, X4) -> U321(X1, X2, X3, X4)
, a__U322(X1, X2, X3, X4) -> U322(X1, X2, X3, X4)
, a__U323(X1, X2, X3, X4) -> U323(X1, X2, X3, X4)
, a__U324(X1, X2, X3, X4) -> U324(X1, X2, X3, X4)
, a__U325(X1, X2, X3, X4) -> U325(X1, X2, X3, X4)
, a__U326(X1, X2, X3, X4) -> U326(X1, X2, X3, X4)
, a__U327(X1, X2) -> U327(X1, X2)
, a__U34(X1, X2) -> U34(X1, X2)
, a__U331(X1, X2, X3) -> U331(X1, X2, X3)
, a__U332(X1, X2) -> U332(X1, X2)
, a__U333(X1, X2) -> U333(X1, X2)
, a__U334(X1, X2) -> U334(X1, X2)
, a__U341(X1, X2, X3) -> U341(X1, X2, X3)
, a__U342(X1, X2, X3) -> U342(X1, X2, X3)
, a__U343(X1, X2, X3) -> U343(X1, X2, X3)
, a__U344(X1, X2, X3) -> U344(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2, X3) -> U42(X1, X2, X3)
, a__U43(X1, X2, X3) -> U43(X1, X2, X3)
, a__U44(X1, X2, X3) -> U44(X1, X2, X3)
, a__U45(X1, X2) -> U45(X1, X2)
, a__U46(X) -> U46(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2, X3) -> U52(X1, X2, X3)
, a__U53(X1, X2, X3) -> U53(X1, X2, X3)
, a__U54(X1, X2, X3) -> U54(X1, X2, X3)
, a__U55(X1, X2) -> U55(X1, X2)
, a__U56(X) -> U56(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X1, X2) -> U62(X1, X2)
, a__isPLNatKind(X) -> isPLNatKind(X)
, a__U63(X) -> U63(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X1, X2) -> U72(X1, X2)
, a__U73(X) -> U73(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X1, X2) -> U82(X1, X2)
, a__U83(X) -> U83(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X1, X2) -> U92(X1, X2)
, a__U93(X) -> U93(X)
, a__tail(X) -> tail(X)
, a__take(X1, X2) -> take(X1, X2)
, a__sel(X1, X2) -> sel(X1, X2)}
StartTerms: basic terms
Strategy: innermost
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..