Problem Transformed CSR 04 LISTUTILITIES complete-noand Z

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES complete-noand Z

stdout:

MAYBE

Problem:
U101(tt(),V1,V2) -> U102(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U102(tt(),V1,V2) -> U103(isLNatKind(activate(V2)),activate(V1),activate(V2))
U103(tt(),V1,V2) -> U104(isLNatKind(activate(V2)),activate(V1),activate(V2))
U104(tt(),V1,V2) -> U105(isNatural(activate(V1)),activate(V2))
U105(tt(),V2) -> U106(isLNat(activate(V2)))
U106(tt()) -> tt()
U11(tt(),N,XS) -> U12(isNaturalKind(activate(N)),activate(N),activate(XS))
U111(tt(),V2) -> U112(isLNatKind(activate(V2)))
U112(tt()) -> tt()
U12(tt(),N,XS) -> U13(isLNat(activate(XS)),activate(N),activate(XS))
U121(tt(),V2) -> U122(isLNatKind(activate(V2)))
U122(tt()) -> tt()
U13(tt(),N,XS) -> U14(isLNatKind(activate(XS)),activate(N),activate(XS))
U131(tt()) -> tt()
U14(tt(),N,XS) -> snd(splitAt(activate(N),activate(XS)))
U141(tt()) -> tt()
U151(tt()) -> tt()
U161(tt()) -> tt()
U171(tt(),V2) -> U172(isLNatKind(activate(V2)))
U172(tt()) -> tt()
U181(tt(),V1) -> U182(isLNatKind(activate(V1)),activate(V1))
U182(tt(),V1) -> U183(isLNat(activate(V1)))
U183(tt()) -> tt()
U191(tt(),V1) -> U192(isNaturalKind(activate(V1)),activate(V1))
U192(tt(),V1) -> U193(isNatural(activate(V1)))
U193(tt()) -> tt()
U201(tt(),V1,V2) -> U202(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U202(tt(),V1,V2) -> U203(isLNatKind(activate(V2)),activate(V1),activate(V2))
U203(tt(),V1,V2) -> U204(isLNatKind(activate(V2)),activate(V1),activate(V2))
U204(tt(),V1,V2) -> U205(isNatural(activate(V1)),activate(V2))
U205(tt(),V2) -> U206(isLNat(activate(V2)))
U206(tt()) -> tt()
U21(tt(),X,Y) -> U22(isLNatKind(activate(X)),activate(X),activate(Y))
U211(tt()) -> tt()
U22(tt(),X,Y) -> U23(isLNat(activate(Y)),activate(X),activate(Y))
U221(tt()) -> tt()
U23(tt(),X,Y) -> U24(isLNatKind(activate(Y)),activate(X))
U231(tt(),V2) -> U232(isLNatKind(activate(V2)))
U232(tt()) -> tt()
U24(tt(),X) -> activate(X)
U241(tt(),V1,V2) -> U242(isLNatKind(activate(V1)),activate(V1),activate(V2))
U242(tt(),V1,V2) -> U243(isLNatKind(activate(V2)),activate(V1),activate(V2))
U243(tt(),V1,V2) -> U244(isLNatKind(activate(V2)),activate(V1),activate(V2))
U244(tt(),V1,V2) -> U245(isLNat(activate(V1)),activate(V2))
U245(tt(),V2) -> U246(isLNat(activate(V2)))
U246(tt()) -> tt()
U251(tt(),V1,V2) -> U252(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U252(tt(),V1,V2) -> U253(isLNatKind(activate(V2)),activate(V1),activate(V2))
U253(tt(),V1,V2) -> U254(isLNatKind(activate(V2)),activate(V1),activate(V2))
U254(tt(),V1,V2) -> U255(isNatural(activate(V1)),activate(V2))
U255(tt(),V2) -> U256(isLNat(activate(V2)))
U256(tt()) -> tt()
U261(tt(),V2) -> U262(isLNatKind(activate(V2)))
U262(tt()) -> tt()
U271(tt(),V2) -> U272(isLNatKind(activate(V2)))
U272(tt()) -> tt()
U281(tt(),N) -> U282(isNaturalKind(activate(N)),activate(N))
U282(tt(),N) -> cons(activate(N),n__natsFrom(s(activate(N))))
U291(tt(),N,XS) -> U292(isNaturalKind(activate(N)),activate(N),activate(XS))
U292(tt(),N,XS) -> U293(isLNat(activate(XS)),activate(N),activate(XS))
U293(tt(),N,XS) -> U294(isLNatKind(activate(XS)),activate(N),activate(XS))
U294(tt(),N,XS) -> head(afterNth(activate(N),activate(XS)))
U301(tt(),X,Y) -> U302(isLNatKind(activate(X)),activate(Y))
U302(tt(),Y) -> U303(isLNat(activate(Y)),activate(Y))
U303(tt(),Y) -> U304(isLNatKind(activate(Y)),activate(Y))
U304(tt(),Y) -> activate(Y)
U31(tt(),N,XS) -> U32(isNaturalKind(activate(N)),activate(N),activate(XS))
U311(tt(),XS) -> U312(isLNatKind(activate(XS)),activate(XS))
U312(tt(),XS) -> pair(nil(),activate(XS))
U32(tt(),N,XS) -> U33(isLNat(activate(XS)),activate(N),activate(XS))
U321(tt(),N,X,XS) -> U322(isNaturalKind(activate(N)),activate(N),activate(X),activate(XS))
U322(tt(),N,X,XS) -> U323(isNatural(activate(X)),activate(N),activate(X),activate(XS))
U323(tt(),N,X,XS) -> U324(isNaturalKind(activate(X)),activate(N),activate(X),activate(XS))
U324(tt(),N,X,XS) -> U325(isLNat(activate(XS)),activate(N),activate(X),activate(XS))
U325(tt(),N,X,XS) -> U326(isLNatKind(activate(XS)),activate(N),activate(X),activate(XS))
U326(tt(),N,X,XS) -> U327(splitAt(activate(N),activate(XS)),activate(X))
U327(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
U33(tt(),N,XS) -> U34(isLNatKind(activate(XS)),activate(N))
U331(tt(),N,XS) -> U332(isNaturalKind(activate(N)),activate(XS))
U332(tt(),XS) -> U333(isLNat(activate(XS)),activate(XS))
U333(tt(),XS) -> U334(isLNatKind(activate(XS)),activate(XS))
U334(tt(),XS) -> activate(XS)
U34(tt(),N) -> activate(N)
U341(tt(),N,XS) -> U342(isNaturalKind(activate(N)),activate(N),activate(XS))
U342(tt(),N,XS) -> U343(isLNat(activate(XS)),activate(N),activate(XS))
U343(tt(),N,XS) -> U344(isLNatKind(activate(XS)),activate(N),activate(XS))
U344(tt(),N,XS) -> fst(splitAt(activate(N),activate(XS)))
U41(tt(),V1,V2) -> U42(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U42(tt(),V1,V2) -> U43(isLNatKind(activate(V2)),activate(V1),activate(V2))
U43(tt(),V1,V2) -> U44(isLNatKind(activate(V2)),activate(V1),activate(V2))
U44(tt(),V1,V2) -> U45(isNatural(activate(V1)),activate(V2))
U45(tt(),V2) -> U46(isLNat(activate(V2)))
U46(tt()) -> tt()
U51(tt(),V1,V2) -> U52(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U52(tt(),V1,V2) -> U53(isLNatKind(activate(V2)),activate(V1),activate(V2))
U53(tt(),V1,V2) -> U54(isLNatKind(activate(V2)),activate(V1),activate(V2))
U54(tt(),V1,V2) -> U55(isNatural(activate(V1)),activate(V2))
U55(tt(),V2) -> U56(isLNat(activate(V2)))
U56(tt()) -> tt()
U61(tt(),V1) -> U62(isPLNatKind(activate(V1)),activate(V1))
U62(tt(),V1) -> U63(isPLNat(activate(V1)))
U63(tt()) -> tt()
U71(tt(),V1) -> U72(isNaturalKind(activate(V1)),activate(V1))
U72(tt(),V1) -> U73(isNatural(activate(V1)))
U73(tt()) -> tt()
U81(tt(),V1) -> U82(isPLNatKind(activate(V1)),activate(V1))
U82(tt(),V1) -> U83(isPLNat(activate(V1)))
U83(tt()) -> tt()
U91(tt(),V1) -> U92(isLNatKind(activate(V1)),activate(V1))
U92(tt(),V1) -> U93(isLNat(activate(V1)))
U93(tt()) -> tt()
afterNth(N,XS) -> U11(isNatural(N),N,XS)
fst(pair(X,Y)) -> U21(isLNat(X),X,Y)
head(cons(N,XS)) -> U31(isNatural(N),N,activate(XS))
isLNat(n__nil()) -> tt()
isLNat(n__afterNth(V1,V2)) -> U41(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isLNat(n__cons(V1,V2)) -> U51(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isLNat(n__fst(V1)) -> U61(isPLNatKind(activate(V1)),activate(V1))
isLNat(n__natsFrom(V1)) -> U71(isNaturalKind(activate(V1)),activate(V1))
isLNat(n__snd(V1)) -> U81(isPLNatKind(activate(V1)),activate(V1))
isLNat(n__tail(V1)) -> U91(isLNatKind(activate(V1)),activate(V1))
isLNat(n__take(V1,V2)) -> U101(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isLNatKind(n__nil()) -> tt()
isLNatKind(n__afterNth(V1,V2)) -> U111(isNaturalKind(activate(V1)),activate(V2))
isLNatKind(n__cons(V1,V2)) -> U121(isNaturalKind(activate(V1)),activate(V2))
isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1)))
isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1)))
isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1)))
isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1)))
isLNatKind(n__take(V1,V2)) -> U171(isNaturalKind(activate(V1)),activate(V2))
isNatural(n__0()) -> tt()
isNatural(n__head(V1)) -> U181(isLNatKind(activate(V1)),activate(V1))
isNatural(n__s(V1)) -> U191(isNaturalKind(activate(V1)),activate(V1))
isNatural(n__sel(V1,V2)) -> U201(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isNaturalKind(n__0()) -> tt()
isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1)))
isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1)))
isNaturalKind(n__sel(V1,V2)) -> U231(isNaturalKind(activate(V1)),activate(V2))
isPLNat(n__pair(V1,V2)) -> U241(isLNatKind(activate(V1)),activate(V1),activate(V2))
isPLNat(n__splitAt(V1,V2)) -> U251(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isPLNatKind(n__pair(V1,V2)) -> U261(isLNatKind(activate(V1)),activate(V2))
isPLNatKind(n__splitAt(V1,V2)) -> U271(isNaturalKind(activate(V1)),activate(V2))
natsFrom(N) -> U281(isNatural(N),N)
sel(N,XS) -> U291(isNatural(N),N,XS)
snd(pair(X,Y)) -> U301(isLNat(X),X,Y)
splitAt(0(),XS) -> U311(isLNat(XS),XS)
splitAt(s(N),cons(X,XS)) -> U321(isNatural(N),N,X,activate(XS))
tail(cons(N,XS)) -> U331(isNatural(N),N,activate(XS))
take(N,XS) -> U341(isNatural(N),N,XS)
natsFrom(X) -> n__natsFrom(X)
nil() -> n__nil()
afterNth(X1,X2) -> n__afterNth(X1,X2)
cons(X1,X2) -> n__cons(X1,X2)
fst(X) -> n__fst(X)
snd(X) -> n__snd(X)
tail(X) -> n__tail(X)
take(X1,X2) -> n__take(X1,X2)
0() -> n__0()
head(X) -> n__head(X)
s(X) -> n__s(X)
sel(X1,X2) -> n__sel(X1,X2)
pair(X1,X2) -> n__pair(X1,X2)
splitAt(X1,X2) -> n__splitAt(X1,X2)
activate(n__natsFrom(X)) -> natsFrom(X)
activate(n__nil()) -> nil()
activate(n__afterNth(X1,X2)) -> afterNth(X1,X2)
activate(n__cons(X1,X2)) -> cons(X1,X2)
activate(n__fst(X)) -> fst(X)
activate(n__snd(X)) -> snd(X)
activate(n__tail(X)) -> tail(X)
activate(n__take(X1,X2)) -> take(X1,X2)
activate(n__0()) -> 0()
activate(n__head(X)) -> head(X)
activate(n__s(X)) -> s(X)
activate(n__sel(X1,X2)) -> sel(X1,X2)
activate(n__pair(X1,X2)) -> pair(X1,X2)
activate(n__splitAt(X1,X2)) -> splitAt(X1,X2)
activate(X) -> X

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES complete-noand Z

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES complete-noand Z

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  U101(tt(), V1, V2) ->
       U102(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U102(tt(), V1, V2) ->
       U103(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U103(tt(), V1, V2) ->
       U104(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2))
     , U105(tt(), V2) -> U106(isLNat(activate(V2)))
     , U106(tt()) -> tt()
     , U11(tt(), N, XS) ->
       U12(isNaturalKind(activate(N)), activate(N), activate(XS))
     , U111(tt(), V2) -> U112(isLNatKind(activate(V2)))
     , U112(tt()) -> tt()
     , U12(tt(), N, XS) ->
       U13(isLNat(activate(XS)), activate(N), activate(XS))
     , U121(tt(), V2) -> U122(isLNatKind(activate(V2)))
     , U122(tt()) -> tt()
     , U13(tt(), N, XS) ->
       U14(isLNatKind(activate(XS)), activate(N), activate(XS))
     , U131(tt()) -> tt()
     , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS)))
     , U141(tt()) -> tt()
     , U151(tt()) -> tt()
     , U161(tt()) -> tt()
     , U171(tt(), V2) -> U172(isLNatKind(activate(V2)))
     , U172(tt()) -> tt()
     , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1))
     , U182(tt(), V1) -> U183(isLNat(activate(V1)))
     , U183(tt()) -> tt()
     , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1))
     , U192(tt(), V1) -> U193(isNatural(activate(V1)))
     , U193(tt()) -> tt()
     , U201(tt(), V1, V2) ->
       U202(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U202(tt(), V1, V2) ->
       U203(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U203(tt(), V1, V2) ->
       U204(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2))
     , U205(tt(), V2) -> U206(isLNat(activate(V2)))
     , U206(tt()) -> tt()
     , U21(tt(), X, Y) ->
       U22(isLNatKind(activate(X)), activate(X), activate(Y))
     , U211(tt()) -> tt()
     , U22(tt(), X, Y) ->
       U23(isLNat(activate(Y)), activate(X), activate(Y))
     , U221(tt()) -> tt()
     , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X))
     , U231(tt(), V2) -> U232(isLNatKind(activate(V2)))
     , U232(tt()) -> tt()
     , U24(tt(), X) -> activate(X)
     , U241(tt(), V1, V2) ->
       U242(isLNatKind(activate(V1)), activate(V1), activate(V2))
     , U242(tt(), V1, V2) ->
       U243(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U243(tt(), V1, V2) ->
       U244(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2))
     , U245(tt(), V2) -> U246(isLNat(activate(V2)))
     , U246(tt()) -> tt()
     , U251(tt(), V1, V2) ->
       U252(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U252(tt(), V1, V2) ->
       U253(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U253(tt(), V1, V2) ->
       U254(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2))
     , U255(tt(), V2) -> U256(isLNat(activate(V2)))
     , U256(tt()) -> tt()
     , U261(tt(), V2) -> U262(isLNatKind(activate(V2)))
     , U262(tt()) -> tt()
     , U271(tt(), V2) -> U272(isLNatKind(activate(V2)))
     , U272(tt()) -> tt()
     , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N))
     , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N))))
     , U291(tt(), N, XS) ->
       U292(isNaturalKind(activate(N)), activate(N), activate(XS))
     , U292(tt(), N, XS) ->
       U293(isLNat(activate(XS)), activate(N), activate(XS))
     , U293(tt(), N, XS) ->
       U294(isLNatKind(activate(XS)), activate(N), activate(XS))
     , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS)))
     , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y))
     , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y))
     , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y))
     , U304(tt(), Y) -> activate(Y)
     , U31(tt(), N, XS) ->
       U32(isNaturalKind(activate(N)), activate(N), activate(XS))
     , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS))
     , U312(tt(), XS) -> pair(nil(), activate(XS))
     , U32(tt(), N, XS) ->
       U33(isLNat(activate(XS)), activate(N), activate(XS))
     , U321(tt(), N, X, XS) ->
       U322(isNaturalKind(activate(N)),
            activate(N),
            activate(X),
            activate(XS))
     , U322(tt(), N, X, XS) ->
       U323(isNatural(activate(X)),
            activate(N),
            activate(X),
            activate(XS))
     , U323(tt(), N, X, XS) ->
       U324(isNaturalKind(activate(X)),
            activate(N),
            activate(X),
            activate(XS))
     , U324(tt(), N, X, XS) ->
       U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS))
     , U325(tt(), N, X, XS) ->
       U326(isLNatKind(activate(XS)),
            activate(N),
            activate(X),
            activate(XS))
     , U326(tt(), N, X, XS) ->
       U327(splitAt(activate(N), activate(XS)), activate(X))
     , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
     , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N))
     , U331(tt(), N, XS) ->
       U332(isNaturalKind(activate(N)), activate(XS))
     , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS))
     , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS))
     , U334(tt(), XS) -> activate(XS)
     , U34(tt(), N) -> activate(N)
     , U341(tt(), N, XS) ->
       U342(isNaturalKind(activate(N)), activate(N), activate(XS))
     , U342(tt(), N, XS) ->
       U343(isLNat(activate(XS)), activate(N), activate(XS))
     , U343(tt(), N, XS) ->
       U344(isLNatKind(activate(XS)), activate(N), activate(XS))
     , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS)))
     , U41(tt(), V1, V2) ->
       U42(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U42(tt(), V1, V2) ->
       U43(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U43(tt(), V1, V2) ->
       U44(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2))
     , U45(tt(), V2) -> U46(isLNat(activate(V2)))
     , U46(tt()) -> tt()
     , U51(tt(), V1, V2) ->
       U52(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U52(tt(), V1, V2) ->
       U53(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U53(tt(), V1, V2) ->
       U54(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2))
     , U55(tt(), V2) -> U56(isLNat(activate(V2)))
     , U56(tt()) -> tt()
     , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1))
     , U62(tt(), V1) -> U63(isPLNat(activate(V1)))
     , U63(tt()) -> tt()
     , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1))
     , U72(tt(), V1) -> U73(isNatural(activate(V1)))
     , U73(tt()) -> tt()
     , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1))
     , U82(tt(), V1) -> U83(isPLNat(activate(V1)))
     , U83(tt()) -> tt()
     , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1))
     , U92(tt(), V1) -> U93(isLNat(activate(V1)))
     , U93(tt()) -> tt()
     , afterNth(N, XS) -> U11(isNatural(N), N, XS)
     , fst(pair(X, Y)) -> U21(isLNat(X), X, Y)
     , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS))
     , isLNat(n__nil()) -> tt()
     , isLNat(n__afterNth(V1, V2)) ->
       U41(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isLNat(n__cons(V1, V2)) ->
       U51(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isLNat(n__fst(V1)) ->
       U61(isPLNatKind(activate(V1)), activate(V1))
     , isLNat(n__natsFrom(V1)) ->
       U71(isNaturalKind(activate(V1)), activate(V1))
     , isLNat(n__snd(V1)) ->
       U81(isPLNatKind(activate(V1)), activate(V1))
     , isLNat(n__tail(V1)) ->
       U91(isLNatKind(activate(V1)), activate(V1))
     , isLNat(n__take(V1, V2)) ->
       U101(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isLNatKind(n__nil()) -> tt()
     , isLNatKind(n__afterNth(V1, V2)) ->
       U111(isNaturalKind(activate(V1)), activate(V2))
     , isLNatKind(n__cons(V1, V2)) ->
       U121(isNaturalKind(activate(V1)), activate(V2))
     , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1)))
     , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1)))
     , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1)))
     , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1)))
     , isLNatKind(n__take(V1, V2)) ->
       U171(isNaturalKind(activate(V1)), activate(V2))
     , isNatural(n__0()) -> tt()
     , isNatural(n__head(V1)) ->
       U181(isLNatKind(activate(V1)), activate(V1))
     , isNatural(n__s(V1)) ->
       U191(isNaturalKind(activate(V1)), activate(V1))
     , isNatural(n__sel(V1, V2)) ->
       U201(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isNaturalKind(n__0()) -> tt()
     , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1)))
     , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1)))
     , isNaturalKind(n__sel(V1, V2)) ->
       U231(isNaturalKind(activate(V1)), activate(V2))
     , isPLNat(n__pair(V1, V2)) ->
       U241(isLNatKind(activate(V1)), activate(V1), activate(V2))
     , isPLNat(n__splitAt(V1, V2)) ->
       U251(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isPLNatKind(n__pair(V1, V2)) ->
       U261(isLNatKind(activate(V1)), activate(V2))
     , isPLNatKind(n__splitAt(V1, V2)) ->
       U271(isNaturalKind(activate(V1)), activate(V2))
     , natsFrom(N) -> U281(isNatural(N), N)
     , sel(N, XS) -> U291(isNatural(N), N, XS)
     , snd(pair(X, Y)) -> U301(isLNat(X), X, Y)
     , splitAt(0(), XS) -> U311(isLNat(XS), XS)
     , splitAt(s(N), cons(X, XS)) ->
       U321(isNatural(N), N, X, activate(XS))
     , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS))
     , take(N, XS) -> U341(isNatural(N), N, XS)
     , natsFrom(X) -> n__natsFrom(X)
     , nil() -> n__nil()
     , afterNth(X1, X2) -> n__afterNth(X1, X2)
     , cons(X1, X2) -> n__cons(X1, X2)
     , fst(X) -> n__fst(X)
     , snd(X) -> n__snd(X)
     , tail(X) -> n__tail(X)
     , take(X1, X2) -> n__take(X1, X2)
     , 0() -> n__0()
     , head(X) -> n__head(X)
     , s(X) -> n__s(X)
     , sel(X1, X2) -> n__sel(X1, X2)
     , pair(X1, X2) -> n__pair(X1, X2)
     , splitAt(X1, X2) -> n__splitAt(X1, X2)
     , activate(n__natsFrom(X)) -> natsFrom(X)
     , activate(n__nil()) -> nil()
     , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2)
     , activate(n__cons(X1, X2)) -> cons(X1, X2)
     , activate(n__fst(X)) -> fst(X)
     , activate(n__snd(X)) -> snd(X)
     , activate(n__tail(X)) -> tail(X)
     , activate(n__take(X1, X2)) -> take(X1, X2)
     , activate(n__0()) -> 0()
     , activate(n__head(X)) -> head(X)
     , activate(n__s(X)) -> s(X)
     , activate(n__sel(X1, X2)) -> sel(X1, X2)
     , activate(n__pair(X1, X2)) -> pair(X1, X2)
     , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2)
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES complete-noand Z

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES complete-noand Z

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  U101(tt(), V1, V2) ->
       U102(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U102(tt(), V1, V2) ->
       U103(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U103(tt(), V1, V2) ->
       U104(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U104(tt(), V1, V2) -> U105(isNatural(activate(V1)), activate(V2))
     , U105(tt(), V2) -> U106(isLNat(activate(V2)))
     , U106(tt()) -> tt()
     , U11(tt(), N, XS) ->
       U12(isNaturalKind(activate(N)), activate(N), activate(XS))
     , U111(tt(), V2) -> U112(isLNatKind(activate(V2)))
     , U112(tt()) -> tt()
     , U12(tt(), N, XS) ->
       U13(isLNat(activate(XS)), activate(N), activate(XS))
     , U121(tt(), V2) -> U122(isLNatKind(activate(V2)))
     , U122(tt()) -> tt()
     , U13(tt(), N, XS) ->
       U14(isLNatKind(activate(XS)), activate(N), activate(XS))
     , U131(tt()) -> tt()
     , U14(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS)))
     , U141(tt()) -> tt()
     , U151(tt()) -> tt()
     , U161(tt()) -> tt()
     , U171(tt(), V2) -> U172(isLNatKind(activate(V2)))
     , U172(tt()) -> tt()
     , U181(tt(), V1) -> U182(isLNatKind(activate(V1)), activate(V1))
     , U182(tt(), V1) -> U183(isLNat(activate(V1)))
     , U183(tt()) -> tt()
     , U191(tt(), V1) -> U192(isNaturalKind(activate(V1)), activate(V1))
     , U192(tt(), V1) -> U193(isNatural(activate(V1)))
     , U193(tt()) -> tt()
     , U201(tt(), V1, V2) ->
       U202(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U202(tt(), V1, V2) ->
       U203(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U203(tt(), V1, V2) ->
       U204(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U204(tt(), V1, V2) -> U205(isNatural(activate(V1)), activate(V2))
     , U205(tt(), V2) -> U206(isLNat(activate(V2)))
     , U206(tt()) -> tt()
     , U21(tt(), X, Y) ->
       U22(isLNatKind(activate(X)), activate(X), activate(Y))
     , U211(tt()) -> tt()
     , U22(tt(), X, Y) ->
       U23(isLNat(activate(Y)), activate(X), activate(Y))
     , U221(tt()) -> tt()
     , U23(tt(), X, Y) -> U24(isLNatKind(activate(Y)), activate(X))
     , U231(tt(), V2) -> U232(isLNatKind(activate(V2)))
     , U232(tt()) -> tt()
     , U24(tt(), X) -> activate(X)
     , U241(tt(), V1, V2) ->
       U242(isLNatKind(activate(V1)), activate(V1), activate(V2))
     , U242(tt(), V1, V2) ->
       U243(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U243(tt(), V1, V2) ->
       U244(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U244(tt(), V1, V2) -> U245(isLNat(activate(V1)), activate(V2))
     , U245(tt(), V2) -> U246(isLNat(activate(V2)))
     , U246(tt()) -> tt()
     , U251(tt(), V1, V2) ->
       U252(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U252(tt(), V1, V2) ->
       U253(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U253(tt(), V1, V2) ->
       U254(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U254(tt(), V1, V2) -> U255(isNatural(activate(V1)), activate(V2))
     , U255(tt(), V2) -> U256(isLNat(activate(V2)))
     , U256(tt()) -> tt()
     , U261(tt(), V2) -> U262(isLNatKind(activate(V2)))
     , U262(tt()) -> tt()
     , U271(tt(), V2) -> U272(isLNatKind(activate(V2)))
     , U272(tt()) -> tt()
     , U281(tt(), N) -> U282(isNaturalKind(activate(N)), activate(N))
     , U282(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N))))
     , U291(tt(), N, XS) ->
       U292(isNaturalKind(activate(N)), activate(N), activate(XS))
     , U292(tt(), N, XS) ->
       U293(isLNat(activate(XS)), activate(N), activate(XS))
     , U293(tt(), N, XS) ->
       U294(isLNatKind(activate(XS)), activate(N), activate(XS))
     , U294(tt(), N, XS) -> head(afterNth(activate(N), activate(XS)))
     , U301(tt(), X, Y) -> U302(isLNatKind(activate(X)), activate(Y))
     , U302(tt(), Y) -> U303(isLNat(activate(Y)), activate(Y))
     , U303(tt(), Y) -> U304(isLNatKind(activate(Y)), activate(Y))
     , U304(tt(), Y) -> activate(Y)
     , U31(tt(), N, XS) ->
       U32(isNaturalKind(activate(N)), activate(N), activate(XS))
     , U311(tt(), XS) -> U312(isLNatKind(activate(XS)), activate(XS))
     , U312(tt(), XS) -> pair(nil(), activate(XS))
     , U32(tt(), N, XS) ->
       U33(isLNat(activate(XS)), activate(N), activate(XS))
     , U321(tt(), N, X, XS) ->
       U322(isNaturalKind(activate(N)),
            activate(N),
            activate(X),
            activate(XS))
     , U322(tt(), N, X, XS) ->
       U323(isNatural(activate(X)),
            activate(N),
            activate(X),
            activate(XS))
     , U323(tt(), N, X, XS) ->
       U324(isNaturalKind(activate(X)),
            activate(N),
            activate(X),
            activate(XS))
     , U324(tt(), N, X, XS) ->
       U325(isLNat(activate(XS)), activate(N), activate(X), activate(XS))
     , U325(tt(), N, X, XS) ->
       U326(isLNatKind(activate(XS)),
            activate(N),
            activate(X),
            activate(XS))
     , U326(tt(), N, X, XS) ->
       U327(splitAt(activate(N), activate(XS)), activate(X))
     , U327(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
     , U33(tt(), N, XS) -> U34(isLNatKind(activate(XS)), activate(N))
     , U331(tt(), N, XS) ->
       U332(isNaturalKind(activate(N)), activate(XS))
     , U332(tt(), XS) -> U333(isLNat(activate(XS)), activate(XS))
     , U333(tt(), XS) -> U334(isLNatKind(activate(XS)), activate(XS))
     , U334(tt(), XS) -> activate(XS)
     , U34(tt(), N) -> activate(N)
     , U341(tt(), N, XS) ->
       U342(isNaturalKind(activate(N)), activate(N), activate(XS))
     , U342(tt(), N, XS) ->
       U343(isLNat(activate(XS)), activate(N), activate(XS))
     , U343(tt(), N, XS) ->
       U344(isLNatKind(activate(XS)), activate(N), activate(XS))
     , U344(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS)))
     , U41(tt(), V1, V2) ->
       U42(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U42(tt(), V1, V2) ->
       U43(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U43(tt(), V1, V2) ->
       U44(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U44(tt(), V1, V2) -> U45(isNatural(activate(V1)), activate(V2))
     , U45(tt(), V2) -> U46(isLNat(activate(V2)))
     , U46(tt()) -> tt()
     , U51(tt(), V1, V2) ->
       U52(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , U52(tt(), V1, V2) ->
       U53(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U53(tt(), V1, V2) ->
       U54(isLNatKind(activate(V2)), activate(V1), activate(V2))
     , U54(tt(), V1, V2) -> U55(isNatural(activate(V1)), activate(V2))
     , U55(tt(), V2) -> U56(isLNat(activate(V2)))
     , U56(tt()) -> tt()
     , U61(tt(), V1) -> U62(isPLNatKind(activate(V1)), activate(V1))
     , U62(tt(), V1) -> U63(isPLNat(activate(V1)))
     , U63(tt()) -> tt()
     , U71(tt(), V1) -> U72(isNaturalKind(activate(V1)), activate(V1))
     , U72(tt(), V1) -> U73(isNatural(activate(V1)))
     , U73(tt()) -> tt()
     , U81(tt(), V1) -> U82(isPLNatKind(activate(V1)), activate(V1))
     , U82(tt(), V1) -> U83(isPLNat(activate(V1)))
     , U83(tt()) -> tt()
     , U91(tt(), V1) -> U92(isLNatKind(activate(V1)), activate(V1))
     , U92(tt(), V1) -> U93(isLNat(activate(V1)))
     , U93(tt()) -> tt()
     , afterNth(N, XS) -> U11(isNatural(N), N, XS)
     , fst(pair(X, Y)) -> U21(isLNat(X), X, Y)
     , head(cons(N, XS)) -> U31(isNatural(N), N, activate(XS))
     , isLNat(n__nil()) -> tt()
     , isLNat(n__afterNth(V1, V2)) ->
       U41(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isLNat(n__cons(V1, V2)) ->
       U51(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isLNat(n__fst(V1)) ->
       U61(isPLNatKind(activate(V1)), activate(V1))
     , isLNat(n__natsFrom(V1)) ->
       U71(isNaturalKind(activate(V1)), activate(V1))
     , isLNat(n__snd(V1)) ->
       U81(isPLNatKind(activate(V1)), activate(V1))
     , isLNat(n__tail(V1)) ->
       U91(isLNatKind(activate(V1)), activate(V1))
     , isLNat(n__take(V1, V2)) ->
       U101(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isLNatKind(n__nil()) -> tt()
     , isLNatKind(n__afterNth(V1, V2)) ->
       U111(isNaturalKind(activate(V1)), activate(V2))
     , isLNatKind(n__cons(V1, V2)) ->
       U121(isNaturalKind(activate(V1)), activate(V2))
     , isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1)))
     , isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1)))
     , isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1)))
     , isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1)))
     , isLNatKind(n__take(V1, V2)) ->
       U171(isNaturalKind(activate(V1)), activate(V2))
     , isNatural(n__0()) -> tt()
     , isNatural(n__head(V1)) ->
       U181(isLNatKind(activate(V1)), activate(V1))
     , isNatural(n__s(V1)) ->
       U191(isNaturalKind(activate(V1)), activate(V1))
     , isNatural(n__sel(V1, V2)) ->
       U201(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isNaturalKind(n__0()) -> tt()
     , isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1)))
     , isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1)))
     , isNaturalKind(n__sel(V1, V2)) ->
       U231(isNaturalKind(activate(V1)), activate(V2))
     , isPLNat(n__pair(V1, V2)) ->
       U241(isLNatKind(activate(V1)), activate(V1), activate(V2))
     , isPLNat(n__splitAt(V1, V2)) ->
       U251(isNaturalKind(activate(V1)), activate(V1), activate(V2))
     , isPLNatKind(n__pair(V1, V2)) ->
       U261(isLNatKind(activate(V1)), activate(V2))
     , isPLNatKind(n__splitAt(V1, V2)) ->
       U271(isNaturalKind(activate(V1)), activate(V2))
     , natsFrom(N) -> U281(isNatural(N), N)
     , sel(N, XS) -> U291(isNatural(N), N, XS)
     , snd(pair(X, Y)) -> U301(isLNat(X), X, Y)
     , splitAt(0(), XS) -> U311(isLNat(XS), XS)
     , splitAt(s(N), cons(X, XS)) ->
       U321(isNatural(N), N, X, activate(XS))
     , tail(cons(N, XS)) -> U331(isNatural(N), N, activate(XS))
     , take(N, XS) -> U341(isNatural(N), N, XS)
     , natsFrom(X) -> n__natsFrom(X)
     , nil() -> n__nil()
     , afterNth(X1, X2) -> n__afterNth(X1, X2)
     , cons(X1, X2) -> n__cons(X1, X2)
     , fst(X) -> n__fst(X)
     , snd(X) -> n__snd(X)
     , tail(X) -> n__tail(X)
     , take(X1, X2) -> n__take(X1, X2)
     , 0() -> n__0()
     , head(X) -> n__head(X)
     , s(X) -> n__s(X)
     , sel(X1, X2) -> n__sel(X1, X2)
     , pair(X1, X2) -> n__pair(X1, X2)
     , splitAt(X1, X2) -> n__splitAt(X1, X2)
     , activate(n__natsFrom(X)) -> natsFrom(X)
     , activate(n__nil()) -> nil()
     , activate(n__afterNth(X1, X2)) -> afterNth(X1, X2)
     , activate(n__cons(X1, X2)) -> cons(X1, X2)
     , activate(n__fst(X)) -> fst(X)
     , activate(n__snd(X)) -> snd(X)
     , activate(n__tail(X)) -> tail(X)
     , activate(n__take(X1, X2)) -> take(X1, X2)
     , activate(n__0()) -> 0()
     , activate(n__head(X)) -> head(X)
     , activate(n__s(X)) -> s(X)
     , activate(n__sel(X1, X2)) -> sel(X1, X2)
     , activate(n__pair(X1, X2)) -> pair(X1, X2)
     , activate(n__splitAt(X1, X2)) -> splitAt(X1, X2)
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds