LMPO
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), V1, V2) -> a__U102(a__isNatural(V1), V2)
, a__U102(tt(), V2) -> a__U103(a__isLNat(V2))
, a__U103(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U111(tt(), V1) -> a__U112(a__isLNat(V1))
, a__U112(tt()) -> tt()
, a__U121(tt(), V1) -> a__U122(a__isNatural(V1))
, a__U122(tt()) -> tt()
, a__U131(tt(), V1, V2) -> a__U132(a__isNatural(V1), V2)
, a__U132(tt(), V2) -> a__U133(a__isLNat(V2))
, a__U133(tt()) -> tt()
, a__U141(tt(), V1, V2) -> a__U142(a__isLNat(V1), V2)
, a__U142(tt(), V2) -> a__U143(a__isLNat(V2))
, a__U143(tt()) -> tt()
, a__U151(tt(), V1, V2) -> a__U152(a__isNatural(V1), V2)
, a__U152(tt(), V2) -> a__U153(a__isLNat(V2))
, a__U153(tt()) -> tt()
, a__U161(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U171(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U181(tt(), Y) -> mark(Y)
, a__U191(tt(), XS) -> pair(nil(), mark(XS))
, a__U201(tt(), N, X, XS) ->
a__U202(a__splitAt(mark(N), mark(XS)), X)
, a__U202(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U21(tt(), X) -> mark(X)
, a__U211(tt(), XS) -> mark(XS)
, a__U221(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U31(tt(), N) -> mark(N)
, a__U41(tt(), V1, V2) -> a__U42(a__isNatural(V1), V2)
, a__U42(tt(), V2) -> a__U43(a__isLNat(V2))
, a__U43(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNatural(V1), V2)
, a__U52(tt(), V2) -> a__U53(a__isLNat(V2))
, a__U53(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNat(V1))
, a__U62(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNatural(V1))
, a__U72(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNat(V1))
, a__U82(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNat(V1))
, a__U92(tt()) -> tt()
, a__afterNth(N, XS) ->
a__U11(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__and(tt(), X) -> mark(X)
, a__fst(pair(X, Y)) ->
a__U21(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
X)
, a__head(cons(N, XS)) ->
a__U31(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNat(cons(V1, V2)) ->
a__U51(a__and(a__isNaturalKind(V1), isLNatKind(V2)), 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__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(cons(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1)
, a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(tail(V1)) -> a__isLNatKind(V1)
, a__isLNatKind(take(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U131(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__isLNatKind(V1)
, a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1)
, a__isNaturalKind(sel(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isPLNat(pair(V1, V2)) ->
a__U141(a__and(a__isLNatKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U151(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNatKind(pair(V1, V2)) ->
a__and(a__isLNatKind(V1), isLNatKind(V2))
, a__isPLNatKind(splitAt(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__natsFrom(N) ->
a__U161(a__and(a__isNatural(N), isNaturalKind(N)), N)
, a__sel(N, XS) ->
a__U171(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__snd(pair(X, Y)) ->
a__U181(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
Y)
, a__splitAt(0(), XS) ->
a__U191(a__and(a__isLNat(XS), isLNatKind(XS)), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U201(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(and(isNatural(X), isNaturalKind(X)),
and(isLNat(XS), isLNatKind(XS)))),
N,
X,
XS)
, a__tail(cons(N, XS)) ->
a__U211(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
XS)
, a__take(N, XS) ->
a__U221(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2)) -> a__U102(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U103(X)) -> a__U103(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3)) -> a__U131(mark(X1), X2, X3)
, mark(U132(X1, X2)) -> a__U132(mark(X1), X2)
, mark(U133(X)) -> a__U133(mark(X))
, mark(U141(X1, X2, X3)) -> a__U141(mark(X1), X2, X3)
, mark(U142(X1, X2)) -> a__U142(mark(X1), X2)
, mark(U143(X)) -> a__U143(mark(X))
, mark(U151(X1, X2, X3)) -> a__U151(mark(X1), X2, X3)
, mark(U152(X1, X2)) -> a__U152(mark(X1), X2)
, mark(U153(X)) -> a__U153(mark(X))
, mark(U161(X1, X2)) -> a__U161(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U171(X1, X2, X3)) -> a__U171(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U201(X1, X2, X3, X4)) -> a__U201(mark(X1), X2, X3, X4)
, mark(U202(X1, X2)) -> a__U202(mark(X1), X2)
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U211(X1, X2)) -> a__U211(mark(X1), X2)
, mark(U221(X1, X2, X3)) -> a__U221(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
, mark(U43(X)) -> a__U43(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
, mark(U53(X)) -> a__U53(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X)) -> a__U72(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X)) -> a__U82(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(isPLNatKind(X)) -> a__isPLNatKind(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) -> U102(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U103(X) -> U103(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3) -> U131(X1, X2, X3)
, a__U132(X1, X2) -> U132(X1, X2)
, a__U133(X) -> U133(X)
, a__U141(X1, X2, X3) -> U141(X1, X2, X3)
, a__U142(X1, X2) -> U142(X1, X2)
, a__U143(X) -> U143(X)
, a__U151(X1, X2, X3) -> U151(X1, X2, X3)
, a__U152(X1, X2) -> U152(X1, X2)
, a__U153(X) -> U153(X)
, a__U161(X1, X2) -> U161(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U171(X1, X2, X3) -> U171(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U201(X1, X2, X3, X4) -> U201(X1, X2, X3, X4)
, a__U202(X1, X2) -> U202(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U211(X1, X2) -> U211(X1, X2)
, a__U221(X1, X2, X3) -> U221(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2) -> U42(X1, X2)
, a__U43(X) -> U43(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2) -> U52(X1, X2)
, a__U53(X) -> U53(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X) -> U72(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X) -> U82(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)
, a__and(X1, X2) -> and(X1, X2)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__isLNatKind(X) -> isLNatKind(X)
, a__isPLNatKind(X) -> isPLNatKind(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*
MAYBE
We consider the following Problem:
Strict Trs:
{ a__U101(tt(), V1, V2) -> a__U102(a__isNatural(V1), V2)
, a__U102(tt(), V2) -> a__U103(a__isLNat(V2))
, a__U103(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U111(tt(), V1) -> a__U112(a__isLNat(V1))
, a__U112(tt()) -> tt()
, a__U121(tt(), V1) -> a__U122(a__isNatural(V1))
, a__U122(tt()) -> tt()
, a__U131(tt(), V1, V2) -> a__U132(a__isNatural(V1), V2)
, a__U132(tt(), V2) -> a__U133(a__isLNat(V2))
, a__U133(tt()) -> tt()
, a__U141(tt(), V1, V2) -> a__U142(a__isLNat(V1), V2)
, a__U142(tt(), V2) -> a__U143(a__isLNat(V2))
, a__U143(tt()) -> tt()
, a__U151(tt(), V1, V2) -> a__U152(a__isNatural(V1), V2)
, a__U152(tt(), V2) -> a__U153(a__isLNat(V2))
, a__U153(tt()) -> tt()
, a__U161(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U171(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U181(tt(), Y) -> mark(Y)
, a__U191(tt(), XS) -> pair(nil(), mark(XS))
, a__U201(tt(), N, X, XS) ->
a__U202(a__splitAt(mark(N), mark(XS)), X)
, a__U202(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U21(tt(), X) -> mark(X)
, a__U211(tt(), XS) -> mark(XS)
, a__U221(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U31(tt(), N) -> mark(N)
, a__U41(tt(), V1, V2) -> a__U42(a__isNatural(V1), V2)
, a__U42(tt(), V2) -> a__U43(a__isLNat(V2))
, a__U43(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNatural(V1), V2)
, a__U52(tt(), V2) -> a__U53(a__isLNat(V2))
, a__U53(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNat(V1))
, a__U62(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNatural(V1))
, a__U72(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNat(V1))
, a__U82(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNat(V1))
, a__U92(tt()) -> tt()
, a__afterNth(N, XS) ->
a__U11(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__and(tt(), X) -> mark(X)
, a__fst(pair(X, Y)) ->
a__U21(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
X)
, a__head(cons(N, XS)) ->
a__U31(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNat(cons(V1, V2)) ->
a__U51(a__and(a__isNaturalKind(V1), isLNatKind(V2)), 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__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(cons(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1)
, a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(tail(V1)) -> a__isLNatKind(V1)
, a__isLNatKind(take(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U131(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__isLNatKind(V1)
, a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1)
, a__isNaturalKind(sel(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isPLNat(pair(V1, V2)) ->
a__U141(a__and(a__isLNatKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U151(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNatKind(pair(V1, V2)) ->
a__and(a__isLNatKind(V1), isLNatKind(V2))
, a__isPLNatKind(splitAt(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__natsFrom(N) ->
a__U161(a__and(a__isNatural(N), isNaturalKind(N)), N)
, a__sel(N, XS) ->
a__U171(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__snd(pair(X, Y)) ->
a__U181(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
Y)
, a__splitAt(0(), XS) ->
a__U191(a__and(a__isLNat(XS), isLNatKind(XS)), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U201(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(and(isNatural(X), isNaturalKind(X)),
and(isLNat(XS), isLNatKind(XS)))),
N,
X,
XS)
, a__tail(cons(N, XS)) ->
a__U211(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
XS)
, a__take(N, XS) ->
a__U221(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2)) -> a__U102(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U103(X)) -> a__U103(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3)) -> a__U131(mark(X1), X2, X3)
, mark(U132(X1, X2)) -> a__U132(mark(X1), X2)
, mark(U133(X)) -> a__U133(mark(X))
, mark(U141(X1, X2, X3)) -> a__U141(mark(X1), X2, X3)
, mark(U142(X1, X2)) -> a__U142(mark(X1), X2)
, mark(U143(X)) -> a__U143(mark(X))
, mark(U151(X1, X2, X3)) -> a__U151(mark(X1), X2, X3)
, mark(U152(X1, X2)) -> a__U152(mark(X1), X2)
, mark(U153(X)) -> a__U153(mark(X))
, mark(U161(X1, X2)) -> a__U161(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U171(X1, X2, X3)) -> a__U171(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U201(X1, X2, X3, X4)) -> a__U201(mark(X1), X2, X3, X4)
, mark(U202(X1, X2)) -> a__U202(mark(X1), X2)
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U211(X1, X2)) -> a__U211(mark(X1), X2)
, mark(U221(X1, X2, X3)) -> a__U221(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
, mark(U43(X)) -> a__U43(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
, mark(U53(X)) -> a__U53(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X)) -> a__U72(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X)) -> a__U82(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(isPLNatKind(X)) -> a__isPLNatKind(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) -> U102(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U103(X) -> U103(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3) -> U131(X1, X2, X3)
, a__U132(X1, X2) -> U132(X1, X2)
, a__U133(X) -> U133(X)
, a__U141(X1, X2, X3) -> U141(X1, X2, X3)
, a__U142(X1, X2) -> U142(X1, X2)
, a__U143(X) -> U143(X)
, a__U151(X1, X2, X3) -> U151(X1, X2, X3)
, a__U152(X1, X2) -> U152(X1, X2)
, a__U153(X) -> U153(X)
, a__U161(X1, X2) -> U161(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U171(X1, X2, X3) -> U171(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U201(X1, X2, X3, X4) -> U201(X1, X2, X3, X4)
, a__U202(X1, X2) -> U202(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U211(X1, X2) -> U211(X1, X2)
, a__U221(X1, X2, X3) -> U221(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2) -> U42(X1, X2)
, a__U43(X) -> U43(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2) -> U52(X1, X2)
, a__U53(X) -> U53(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X) -> U72(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X) -> U82(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)
, a__and(X1, X2) -> and(X1, X2)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__isLNatKind(X) -> isLNatKind(X)
, a__isPLNatKind(X) -> isPLNatKind(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__isNatural(V1), V2)
, a__U102(tt(), V2) -> a__U103(a__isLNat(V2))
, a__U103(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U111(tt(), V1) -> a__U112(a__isLNat(V1))
, a__U112(tt()) -> tt()
, a__U121(tt(), V1) -> a__U122(a__isNatural(V1))
, a__U122(tt()) -> tt()
, a__U131(tt(), V1, V2) -> a__U132(a__isNatural(V1), V2)
, a__U132(tt(), V2) -> a__U133(a__isLNat(V2))
, a__U133(tt()) -> tt()
, a__U141(tt(), V1, V2) -> a__U142(a__isLNat(V1), V2)
, a__U142(tt(), V2) -> a__U143(a__isLNat(V2))
, a__U143(tt()) -> tt()
, a__U151(tt(), V1, V2) -> a__U152(a__isNatural(V1), V2)
, a__U152(tt(), V2) -> a__U153(a__isLNat(V2))
, a__U153(tt()) -> tt()
, a__U161(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U171(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U181(tt(), Y) -> mark(Y)
, a__U191(tt(), XS) -> pair(nil(), mark(XS))
, a__U201(tt(), N, X, XS) ->
a__U202(a__splitAt(mark(N), mark(XS)), X)
, a__U202(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U21(tt(), X) -> mark(X)
, a__U211(tt(), XS) -> mark(XS)
, a__U221(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U31(tt(), N) -> mark(N)
, a__U41(tt(), V1, V2) -> a__U42(a__isNatural(V1), V2)
, a__U42(tt(), V2) -> a__U43(a__isLNat(V2))
, a__U43(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNatural(V1), V2)
, a__U52(tt(), V2) -> a__U53(a__isLNat(V2))
, a__U53(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNat(V1))
, a__U62(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNatural(V1))
, a__U72(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNat(V1))
, a__U82(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNat(V1))
, a__U92(tt()) -> tt()
, a__afterNth(N, XS) ->
a__U11(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__and(tt(), X) -> mark(X)
, a__fst(pair(X, Y)) ->
a__U21(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
X)
, a__head(cons(N, XS)) ->
a__U31(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNat(cons(V1, V2)) ->
a__U51(a__and(a__isNaturalKind(V1), isLNatKind(V2)), 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__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(cons(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1)
, a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(tail(V1)) -> a__isLNatKind(V1)
, a__isLNatKind(take(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U131(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__isLNatKind(V1)
, a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1)
, a__isNaturalKind(sel(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isPLNat(pair(V1, V2)) ->
a__U141(a__and(a__isLNatKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U151(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNatKind(pair(V1, V2)) ->
a__and(a__isLNatKind(V1), isLNatKind(V2))
, a__isPLNatKind(splitAt(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__natsFrom(N) ->
a__U161(a__and(a__isNatural(N), isNaturalKind(N)), N)
, a__sel(N, XS) ->
a__U171(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__snd(pair(X, Y)) ->
a__U181(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
Y)
, a__splitAt(0(), XS) ->
a__U191(a__and(a__isLNat(XS), isLNatKind(XS)), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U201(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(and(isNatural(X), isNaturalKind(X)),
and(isLNat(XS), isLNatKind(XS)))),
N,
X,
XS)
, a__tail(cons(N, XS)) ->
a__U211(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
XS)
, a__take(N, XS) ->
a__U221(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2)) -> a__U102(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U103(X)) -> a__U103(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3)) -> a__U131(mark(X1), X2, X3)
, mark(U132(X1, X2)) -> a__U132(mark(X1), X2)
, mark(U133(X)) -> a__U133(mark(X))
, mark(U141(X1, X2, X3)) -> a__U141(mark(X1), X2, X3)
, mark(U142(X1, X2)) -> a__U142(mark(X1), X2)
, mark(U143(X)) -> a__U143(mark(X))
, mark(U151(X1, X2, X3)) -> a__U151(mark(X1), X2, X3)
, mark(U152(X1, X2)) -> a__U152(mark(X1), X2)
, mark(U153(X)) -> a__U153(mark(X))
, mark(U161(X1, X2)) -> a__U161(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U171(X1, X2, X3)) -> a__U171(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U201(X1, X2, X3, X4)) -> a__U201(mark(X1), X2, X3, X4)
, mark(U202(X1, X2)) -> a__U202(mark(X1), X2)
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U211(X1, X2)) -> a__U211(mark(X1), X2)
, mark(U221(X1, X2, X3)) -> a__U221(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
, mark(U43(X)) -> a__U43(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
, mark(U53(X)) -> a__U53(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X)) -> a__U72(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X)) -> a__U82(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(isPLNatKind(X)) -> a__isPLNatKind(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) -> U102(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U103(X) -> U103(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3) -> U131(X1, X2, X3)
, a__U132(X1, X2) -> U132(X1, X2)
, a__U133(X) -> U133(X)
, a__U141(X1, X2, X3) -> U141(X1, X2, X3)
, a__U142(X1, X2) -> U142(X1, X2)
, a__U143(X) -> U143(X)
, a__U151(X1, X2, X3) -> U151(X1, X2, X3)
, a__U152(X1, X2) -> U152(X1, X2)
, a__U153(X) -> U153(X)
, a__U161(X1, X2) -> U161(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U171(X1, X2, X3) -> U171(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U201(X1, X2, X3, X4) -> U201(X1, X2, X3, X4)
, a__U202(X1, X2) -> U202(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U211(X1, X2) -> U211(X1, X2)
, a__U221(X1, X2, X3) -> U221(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2) -> U42(X1, X2)
, a__U43(X) -> U43(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2) -> U52(X1, X2)
, a__U53(X) -> U53(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X) -> U72(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X) -> U82(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)
, a__and(X1, X2) -> and(X1, X2)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__isLNatKind(X) -> isLNatKind(X)
, a__isPLNatKind(X) -> isPLNatKind(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__isNatural(V1), V2)
, a__U102(tt(), V2) -> a__U103(a__isLNat(V2))
, a__U103(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U111(tt(), V1) -> a__U112(a__isLNat(V1))
, a__U112(tt()) -> tt()
, a__U121(tt(), V1) -> a__U122(a__isNatural(V1))
, a__U122(tt()) -> tt()
, a__U131(tt(), V1, V2) -> a__U132(a__isNatural(V1), V2)
, a__U132(tt(), V2) -> a__U133(a__isLNat(V2))
, a__U133(tt()) -> tt()
, a__U141(tt(), V1, V2) -> a__U142(a__isLNat(V1), V2)
, a__U142(tt(), V2) -> a__U143(a__isLNat(V2))
, a__U143(tt()) -> tt()
, a__U151(tt(), V1, V2) -> a__U152(a__isNatural(V1), V2)
, a__U152(tt(), V2) -> a__U153(a__isLNat(V2))
, a__U153(tt()) -> tt()
, a__U161(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U171(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U181(tt(), Y) -> mark(Y)
, a__U191(tt(), XS) -> pair(nil(), mark(XS))
, a__U201(tt(), N, X, XS) ->
a__U202(a__splitAt(mark(N), mark(XS)), X)
, a__U202(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U21(tt(), X) -> mark(X)
, a__U211(tt(), XS) -> mark(XS)
, a__U221(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U31(tt(), N) -> mark(N)
, a__U41(tt(), V1, V2) -> a__U42(a__isNatural(V1), V2)
, a__U42(tt(), V2) -> a__U43(a__isLNat(V2))
, a__U43(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNatural(V1), V2)
, a__U52(tt(), V2) -> a__U53(a__isLNat(V2))
, a__U53(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNat(V1))
, a__U62(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNatural(V1))
, a__U72(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNat(V1))
, a__U82(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNat(V1))
, a__U92(tt()) -> tt()
, a__afterNth(N, XS) ->
a__U11(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__and(tt(), X) -> mark(X)
, a__fst(pair(X, Y)) ->
a__U21(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
X)
, a__head(cons(N, XS)) ->
a__U31(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNat(cons(V1, V2)) ->
a__U51(a__and(a__isNaturalKind(V1), isLNatKind(V2)), 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__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(cons(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1)
, a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(tail(V1)) -> a__isLNatKind(V1)
, a__isLNatKind(take(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U131(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__isLNatKind(V1)
, a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1)
, a__isNaturalKind(sel(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isPLNat(pair(V1, V2)) ->
a__U141(a__and(a__isLNatKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U151(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNatKind(pair(V1, V2)) ->
a__and(a__isLNatKind(V1), isLNatKind(V2))
, a__isPLNatKind(splitAt(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__natsFrom(N) ->
a__U161(a__and(a__isNatural(N), isNaturalKind(N)), N)
, a__sel(N, XS) ->
a__U171(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__snd(pair(X, Y)) ->
a__U181(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
Y)
, a__splitAt(0(), XS) ->
a__U191(a__and(a__isLNat(XS), isLNatKind(XS)), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U201(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(and(isNatural(X), isNaturalKind(X)),
and(isLNat(XS), isLNatKind(XS)))),
N,
X,
XS)
, a__tail(cons(N, XS)) ->
a__U211(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
XS)
, a__take(N, XS) ->
a__U221(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2)) -> a__U102(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U103(X)) -> a__U103(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3)) -> a__U131(mark(X1), X2, X3)
, mark(U132(X1, X2)) -> a__U132(mark(X1), X2)
, mark(U133(X)) -> a__U133(mark(X))
, mark(U141(X1, X2, X3)) -> a__U141(mark(X1), X2, X3)
, mark(U142(X1, X2)) -> a__U142(mark(X1), X2)
, mark(U143(X)) -> a__U143(mark(X))
, mark(U151(X1, X2, X3)) -> a__U151(mark(X1), X2, X3)
, mark(U152(X1, X2)) -> a__U152(mark(X1), X2)
, mark(U153(X)) -> a__U153(mark(X))
, mark(U161(X1, X2)) -> a__U161(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U171(X1, X2, X3)) -> a__U171(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U201(X1, X2, X3, X4)) -> a__U201(mark(X1), X2, X3, X4)
, mark(U202(X1, X2)) -> a__U202(mark(X1), X2)
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U211(X1, X2)) -> a__U211(mark(X1), X2)
, mark(U221(X1, X2, X3)) -> a__U221(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
, mark(U43(X)) -> a__U43(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
, mark(U53(X)) -> a__U53(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X)) -> a__U72(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X)) -> a__U82(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(isPLNatKind(X)) -> a__isPLNatKind(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) -> U102(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U103(X) -> U103(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3) -> U131(X1, X2, X3)
, a__U132(X1, X2) -> U132(X1, X2)
, a__U133(X) -> U133(X)
, a__U141(X1, X2, X3) -> U141(X1, X2, X3)
, a__U142(X1, X2) -> U142(X1, X2)
, a__U143(X) -> U143(X)
, a__U151(X1, X2, X3) -> U151(X1, X2, X3)
, a__U152(X1, X2) -> U152(X1, X2)
, a__U153(X) -> U153(X)
, a__U161(X1, X2) -> U161(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U171(X1, X2, X3) -> U171(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U201(X1, X2, X3, X4) -> U201(X1, X2, X3, X4)
, a__U202(X1, X2) -> U202(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U211(X1, X2) -> U211(X1, X2)
, a__U221(X1, X2, X3) -> U221(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2) -> U42(X1, X2)
, a__U43(X) -> U43(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2) -> U52(X1, X2)
, a__U53(X) -> U53(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X) -> U72(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X) -> U82(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)
, a__and(X1, X2) -> and(X1, X2)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__isLNatKind(X) -> isLNatKind(X)
, a__isPLNatKind(X) -> isPLNatKind(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__isNatural(V1), V2)
, a__U102(tt(), V2) -> a__U103(a__isLNat(V2))
, a__U103(tt()) -> tt()
, a__U11(tt(), N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
, a__U111(tt(), V1) -> a__U112(a__isLNat(V1))
, a__U112(tt()) -> tt()
, a__U121(tt(), V1) -> a__U122(a__isNatural(V1))
, a__U122(tt()) -> tt()
, a__U131(tt(), V1, V2) -> a__U132(a__isNatural(V1), V2)
, a__U132(tt(), V2) -> a__U133(a__isLNat(V2))
, a__U133(tt()) -> tt()
, a__U141(tt(), V1, V2) -> a__U142(a__isLNat(V1), V2)
, a__U142(tt(), V2) -> a__U143(a__isLNat(V2))
, a__U143(tt()) -> tt()
, a__U151(tt(), V1, V2) -> a__U152(a__isNatural(V1), V2)
, a__U152(tt(), V2) -> a__U153(a__isLNat(V2))
, a__U153(tt()) -> tt()
, a__U161(tt(), N) -> cons(mark(N), natsFrom(s(N)))
, a__U171(tt(), N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
, a__U181(tt(), Y) -> mark(Y)
, a__U191(tt(), XS) -> pair(nil(), mark(XS))
, a__U201(tt(), N, X, XS) ->
a__U202(a__splitAt(mark(N), mark(XS)), X)
, a__U202(pair(YS, ZS), X) -> pair(cons(mark(X), YS), mark(ZS))
, a__U21(tt(), X) -> mark(X)
, a__U211(tt(), XS) -> mark(XS)
, a__U221(tt(), N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
, a__U31(tt(), N) -> mark(N)
, a__U41(tt(), V1, V2) -> a__U42(a__isNatural(V1), V2)
, a__U42(tt(), V2) -> a__U43(a__isLNat(V2))
, a__U43(tt()) -> tt()
, a__U51(tt(), V1, V2) -> a__U52(a__isNatural(V1), V2)
, a__U52(tt(), V2) -> a__U53(a__isLNat(V2))
, a__U53(tt()) -> tt()
, a__U61(tt(), V1) -> a__U62(a__isPLNat(V1))
, a__U62(tt()) -> tt()
, a__U71(tt(), V1) -> a__U72(a__isNatural(V1))
, a__U72(tt()) -> tt()
, a__U81(tt(), V1) -> a__U82(a__isPLNat(V1))
, a__U82(tt()) -> tt()
, a__U91(tt(), V1) -> a__U92(a__isLNat(V1))
, a__U92(tt()) -> tt()
, a__afterNth(N, XS) ->
a__U11(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__and(tt(), X) -> mark(X)
, a__fst(pair(X, Y)) ->
a__U21(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
X)
, a__head(cons(N, XS)) ->
a__U31(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N)
, a__isLNat(nil()) -> tt()
, a__isLNat(afterNth(V1, V2)) ->
a__U41(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNat(cons(V1, V2)) ->
a__U51(a__and(a__isNaturalKind(V1), isLNatKind(V2)), 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__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isLNatKind(nil()) -> tt()
, a__isLNatKind(afterNth(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(cons(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isLNatKind(fst(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(natsFrom(V1)) -> a__isNaturalKind(V1)
, a__isLNatKind(snd(V1)) -> a__isPLNatKind(V1)
, a__isLNatKind(tail(V1)) -> a__isLNatKind(V1)
, a__isLNatKind(take(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isNatural(0()) -> tt()
, a__isNatural(head(V1)) -> a__U111(a__isLNatKind(V1), V1)
, a__isNatural(s(V1)) -> a__U121(a__isNaturalKind(V1), V1)
, a__isNatural(sel(V1, V2)) ->
a__U131(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isNaturalKind(0()) -> tt()
, a__isNaturalKind(head(V1)) -> a__isLNatKind(V1)
, a__isNaturalKind(s(V1)) -> a__isNaturalKind(V1)
, a__isNaturalKind(sel(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__isPLNat(pair(V1, V2)) ->
a__U141(a__and(a__isLNatKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNat(splitAt(V1, V2)) ->
a__U151(a__and(a__isNaturalKind(V1), isLNatKind(V2)), V1, V2)
, a__isPLNatKind(pair(V1, V2)) ->
a__and(a__isLNatKind(V1), isLNatKind(V2))
, a__isPLNatKind(splitAt(V1, V2)) ->
a__and(a__isNaturalKind(V1), isLNatKind(V2))
, a__natsFrom(N) ->
a__U161(a__and(a__isNatural(N), isNaturalKind(N)), N)
, a__sel(N, XS) ->
a__U171(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, a__snd(pair(X, Y)) ->
a__U181(a__and(a__and(a__isLNat(X), isLNatKind(X)),
and(isLNat(Y), isLNatKind(Y))),
Y)
, a__splitAt(0(), XS) ->
a__U191(a__and(a__isLNat(XS), isLNatKind(XS)), XS)
, a__splitAt(s(N), cons(X, XS)) ->
a__U201(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(and(isNatural(X), isNaturalKind(X)),
and(isLNat(XS), isLNatKind(XS)))),
N,
X,
XS)
, a__tail(cons(N, XS)) ->
a__U211(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
XS)
, a__take(N, XS) ->
a__U221(a__and(a__and(a__isNatural(N), isNaturalKind(N)),
and(isLNat(XS), isLNatKind(XS))),
N,
XS)
, mark(U101(X1, X2, X3)) -> a__U101(mark(X1), X2, X3)
, mark(U102(X1, X2)) -> a__U102(mark(X1), X2)
, mark(isNatural(X)) -> a__isNatural(X)
, mark(U103(X)) -> a__U103(mark(X))
, mark(isLNat(X)) -> a__isLNat(X)
, mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
, mark(snd(X)) -> a__snd(mark(X))
, mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
, mark(U111(X1, X2)) -> a__U111(mark(X1), X2)
, mark(U112(X)) -> a__U112(mark(X))
, mark(U121(X1, X2)) -> a__U121(mark(X1), X2)
, mark(U122(X)) -> a__U122(mark(X))
, mark(U131(X1, X2, X3)) -> a__U131(mark(X1), X2, X3)
, mark(U132(X1, X2)) -> a__U132(mark(X1), X2)
, mark(U133(X)) -> a__U133(mark(X))
, mark(U141(X1, X2, X3)) -> a__U141(mark(X1), X2, X3)
, mark(U142(X1, X2)) -> a__U142(mark(X1), X2)
, mark(U143(X)) -> a__U143(mark(X))
, mark(U151(X1, X2, X3)) -> a__U151(mark(X1), X2, X3)
, mark(U152(X1, X2)) -> a__U152(mark(X1), X2)
, mark(U153(X)) -> a__U153(mark(X))
, mark(U161(X1, X2)) -> a__U161(mark(X1), X2)
, mark(natsFrom(X)) -> a__natsFrom(mark(X))
, mark(U171(X1, X2, X3)) -> a__U171(mark(X1), X2, X3)
, mark(head(X)) -> a__head(mark(X))
, mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
, mark(U181(X1, X2)) -> a__U181(mark(X1), X2)
, mark(U191(X1, X2)) -> a__U191(mark(X1), X2)
, mark(U201(X1, X2, X3, X4)) -> a__U201(mark(X1), X2, X3, X4)
, mark(U202(X1, X2)) -> a__U202(mark(X1), X2)
, mark(U21(X1, X2)) -> a__U21(mark(X1), X2)
, mark(U211(X1, X2)) -> a__U211(mark(X1), X2)
, mark(U221(X1, X2, X3)) -> a__U221(mark(X1), X2, X3)
, mark(fst(X)) -> a__fst(mark(X))
, mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
, mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
, mark(U42(X1, X2)) -> a__U42(mark(X1), X2)
, mark(U43(X)) -> a__U43(mark(X))
, mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3)
, mark(U52(X1, X2)) -> a__U52(mark(X1), X2)
, mark(U53(X)) -> a__U53(mark(X))
, mark(U61(X1, X2)) -> a__U61(mark(X1), X2)
, mark(U62(X)) -> a__U62(mark(X))
, mark(isPLNat(X)) -> a__isPLNat(X)
, mark(U71(X1, X2)) -> a__U71(mark(X1), X2)
, mark(U72(X)) -> a__U72(mark(X))
, mark(U81(X1, X2)) -> a__U81(mark(X1), X2)
, mark(U82(X)) -> a__U82(mark(X))
, mark(U91(X1, X2)) -> a__U91(mark(X1), X2)
, mark(U92(X)) -> a__U92(mark(X))
, mark(and(X1, X2)) -> a__and(mark(X1), X2)
, mark(isNaturalKind(X)) -> a__isNaturalKind(X)
, mark(isLNatKind(X)) -> a__isLNatKind(X)
, mark(isPLNatKind(X)) -> a__isPLNatKind(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) -> U102(X1, X2)
, a__isNatural(X) -> isNatural(X)
, a__U103(X) -> U103(X)
, a__isLNat(X) -> isLNat(X)
, a__U11(X1, X2, X3) -> U11(X1, X2, X3)
, a__snd(X) -> snd(X)
, a__splitAt(X1, X2) -> splitAt(X1, X2)
, a__U111(X1, X2) -> U111(X1, X2)
, a__U112(X) -> U112(X)
, a__U121(X1, X2) -> U121(X1, X2)
, a__U122(X) -> U122(X)
, a__U131(X1, X2, X3) -> U131(X1, X2, X3)
, a__U132(X1, X2) -> U132(X1, X2)
, a__U133(X) -> U133(X)
, a__U141(X1, X2, X3) -> U141(X1, X2, X3)
, a__U142(X1, X2) -> U142(X1, X2)
, a__U143(X) -> U143(X)
, a__U151(X1, X2, X3) -> U151(X1, X2, X3)
, a__U152(X1, X2) -> U152(X1, X2)
, a__U153(X) -> U153(X)
, a__U161(X1, X2) -> U161(X1, X2)
, a__natsFrom(X) -> natsFrom(X)
, a__U171(X1, X2, X3) -> U171(X1, X2, X3)
, a__head(X) -> head(X)
, a__afterNth(X1, X2) -> afterNth(X1, X2)
, a__U181(X1, X2) -> U181(X1, X2)
, a__U191(X1, X2) -> U191(X1, X2)
, a__U201(X1, X2, X3, X4) -> U201(X1, X2, X3, X4)
, a__U202(X1, X2) -> U202(X1, X2)
, a__U21(X1, X2) -> U21(X1, X2)
, a__U211(X1, X2) -> U211(X1, X2)
, a__U221(X1, X2, X3) -> U221(X1, X2, X3)
, a__fst(X) -> fst(X)
, a__U31(X1, X2) -> U31(X1, X2)
, a__U41(X1, X2, X3) -> U41(X1, X2, X3)
, a__U42(X1, X2) -> U42(X1, X2)
, a__U43(X) -> U43(X)
, a__U51(X1, X2, X3) -> U51(X1, X2, X3)
, a__U52(X1, X2) -> U52(X1, X2)
, a__U53(X) -> U53(X)
, a__U61(X1, X2) -> U61(X1, X2)
, a__U62(X) -> U62(X)
, a__isPLNat(X) -> isPLNat(X)
, a__U71(X1, X2) -> U71(X1, X2)
, a__U72(X) -> U72(X)
, a__U81(X1, X2) -> U81(X1, X2)
, a__U82(X) -> U82(X)
, a__U91(X1, X2) -> U91(X1, X2)
, a__U92(X) -> U92(X)
, a__and(X1, X2) -> and(X1, X2)
, a__isNaturalKind(X) -> isNaturalKind(X)
, a__isLNatKind(X) -> isLNatKind(X)
, a__isPLNatKind(X) -> isPLNatKind(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..