Problem Transformed CSR 04 LISTUTILITIES nokinds-noand FR

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nokinds-noand FR

stdout:

MAYBE

Problem:
U101(tt(),V2) -> U102(isLNat(activate(V2)))
U102(tt()) -> tt()
U11(tt(),N,XS) -> U12(isLNat(activate(XS)),activate(N),activate(XS))
U111(tt()) -> tt()
U12(tt(),N,XS) -> snd(splitAt(activate(N),activate(XS)))
U121(tt()) -> tt()
U131(tt(),V2) -> U132(isLNat(activate(V2)))
U132(tt()) -> tt()
U141(tt(),V2) -> U142(isLNat(activate(V2)))
U142(tt()) -> tt()
U151(tt(),V2) -> U152(isLNat(activate(V2)))
U152(tt()) -> tt()
U161(tt(),N) -> cons(activate(N),n__natsFrom(n__s(activate(N))))
U171(tt(),N,XS) -> U172(isLNat(activate(XS)),activate(N),activate(XS))
U172(tt(),N,XS) -> head(afterNth(activate(N),activate(XS)))
U181(tt(),Y) -> U182(isLNat(activate(Y)),activate(Y))
U182(tt(),Y) -> activate(Y)
U191(tt(),XS) -> pair(nil(),activate(XS))
U201(tt(),N,X,XS) -> U202(isNatural(activate(X)),activate(N),activate(X),activate(XS))
U202(tt(),N,X,XS) -> U203(isLNat(activate(XS)),activate(N),activate(X),activate(XS))
U203(tt(),N,X,XS) -> U204(splitAt(activate(N),activate(XS)),activate(X))
U204(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
U21(tt(),X,Y) -> U22(isLNat(activate(Y)),activate(X))
U211(tt(),XS) -> U212(isLNat(activate(XS)),activate(XS))
U212(tt(),XS) -> activate(XS)
U22(tt(),X) -> activate(X)
U221(tt(),N,XS) -> U222(isLNat(activate(XS)),activate(N),activate(XS))
U222(tt(),N,XS) -> fst(splitAt(activate(N),activate(XS)))
U31(tt(),N,XS) -> U32(isLNat(activate(XS)),activate(N))
U32(tt(),N) -> activate(N)
U41(tt(),V2) -> U42(isLNat(activate(V2)))
U42(tt()) -> tt()
U51(tt(),V2) -> U52(isLNat(activate(V2)))
U52(tt()) -> tt()
U61(tt()) -> tt()
U71(tt()) -> tt()
U81(tt()) -> tt()
U91(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(isNatural(activate(V1)),activate(V2))
isLNat(n__cons(V1,V2)) -> U51(isNatural(activate(V1)),activate(V2))
isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1)))
isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1)))
isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1)))
isLNat(n__tail(V1)) -> U91(isLNat(activate(V1)))
isLNat(n__take(V1,V2)) -> U101(isNatural(activate(V1)),activate(V2))
isNatural(n__0()) -> tt()
isNatural(n__head(V1)) -> U111(isLNat(activate(V1)))
isNatural(n__s(V1)) -> U121(isNatural(activate(V1)))
isNatural(n__sel(V1,V2)) -> U131(isNatural(activate(V1)),activate(V2))
isPLNat(n__pair(V1,V2)) -> U141(isLNat(activate(V1)),activate(V2))
isPLNat(n__splitAt(V1,V2)) -> U151(isNatural(activate(V1)),activate(V2))
natsFrom(N) -> U161(isNatural(N),N)
sel(N,XS) -> U171(isNatural(N),N,XS)
snd(pair(X,Y)) -> U181(isLNat(X),Y)
splitAt(0(),XS) -> U191(isLNat(XS),XS)
splitAt(s(N),cons(X,XS)) -> U201(isNatural(N),N,X,activate(XS))
tail(cons(N,XS)) -> U211(isNatural(N),activate(XS))
take(N,XS) -> U221(isNatural(N),N,XS)
natsFrom(X) -> n__natsFrom(X)
s(X) -> n__s(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)
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(activate(X))
activate(n__s(X)) -> s(activate(X))
activate(n__nil()) -> nil()
activate(n__afterNth(X1,X2)) -> afterNth(activate(X1),activate(X2))
activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
activate(n__fst(X)) -> fst(activate(X))
activate(n__snd(X)) -> snd(activate(X))
activate(n__tail(X)) -> tail(activate(X))
activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
activate(n__0()) -> 0()
activate(n__head(X)) -> head(activate(X))
activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2))
activate(n__pair(X1,X2)) -> pair(activate(X1),activate(X2))
activate(n__splitAt(X1,X2)) -> splitAt(activate(X1),activate(X2))
activate(X) -> X

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nokinds-noand FR

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES nokinds-noand FR

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  U101(tt(), V2) -> U102(isLNat(activate(V2)))
     , U102(tt()) -> tt()
     , U11(tt(), N, XS) ->
       U12(isLNat(activate(XS)), activate(N), activate(XS))
     , U111(tt()) -> tt()
     , U12(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS)))
     , U121(tt()) -> tt()
     , U131(tt(), V2) -> U132(isLNat(activate(V2)))
     , U132(tt()) -> tt()
     , U141(tt(), V2) -> U142(isLNat(activate(V2)))
     , U142(tt()) -> tt()
     , U151(tt(), V2) -> U152(isLNat(activate(V2)))
     , U152(tt()) -> tt()
     , U161(tt(), N) ->
       cons(activate(N), n__natsFrom(n__s(activate(N))))
     , U171(tt(), N, XS) ->
       U172(isLNat(activate(XS)), activate(N), activate(XS))
     , U172(tt(), N, XS) -> head(afterNth(activate(N), activate(XS)))
     , U181(tt(), Y) -> U182(isLNat(activate(Y)), activate(Y))
     , U182(tt(), Y) -> activate(Y)
     , U191(tt(), XS) -> pair(nil(), activate(XS))
     , U201(tt(), N, X, XS) ->
       U202(isNatural(activate(X)),
            activate(N),
            activate(X),
            activate(XS))
     , U202(tt(), N, X, XS) ->
       U203(isLNat(activate(XS)), activate(N), activate(X), activate(XS))
     , U203(tt(), N, X, XS) ->
       U204(splitAt(activate(N), activate(XS)), activate(X))
     , U204(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
     , U21(tt(), X, Y) -> U22(isLNat(activate(Y)), activate(X))
     , U211(tt(), XS) -> U212(isLNat(activate(XS)), activate(XS))
     , U212(tt(), XS) -> activate(XS)
     , U22(tt(), X) -> activate(X)
     , U221(tt(), N, XS) ->
       U222(isLNat(activate(XS)), activate(N), activate(XS))
     , U222(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS)))
     , U31(tt(), N, XS) -> U32(isLNat(activate(XS)), activate(N))
     , U32(tt(), N) -> activate(N)
     , U41(tt(), V2) -> U42(isLNat(activate(V2)))
     , U42(tt()) -> tt()
     , U51(tt(), V2) -> U52(isLNat(activate(V2)))
     , U52(tt()) -> tt()
     , U61(tt()) -> tt()
     , U71(tt()) -> tt()
     , U81(tt()) -> tt()
     , U91(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(isNatural(activate(V1)), activate(V2))
     , isLNat(n__cons(V1, V2)) ->
       U51(isNatural(activate(V1)), activate(V2))
     , isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1)))
     , isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1)))
     , isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1)))
     , isLNat(n__tail(V1)) -> U91(isLNat(activate(V1)))
     , isLNat(n__take(V1, V2)) ->
       U101(isNatural(activate(V1)), activate(V2))
     , isNatural(n__0()) -> tt()
     , isNatural(n__head(V1)) -> U111(isLNat(activate(V1)))
     , isNatural(n__s(V1)) -> U121(isNatural(activate(V1)))
     , isNatural(n__sel(V1, V2)) ->
       U131(isNatural(activate(V1)), activate(V2))
     , isPLNat(n__pair(V1, V2)) ->
       U141(isLNat(activate(V1)), activate(V2))
     , isPLNat(n__splitAt(V1, V2)) ->
       U151(isNatural(activate(V1)), activate(V2))
     , natsFrom(N) -> U161(isNatural(N), N)
     , sel(N, XS) -> U171(isNatural(N), N, XS)
     , snd(pair(X, Y)) -> U181(isLNat(X), Y)
     , splitAt(0(), XS) -> U191(isLNat(XS), XS)
     , splitAt(s(N), cons(X, XS)) ->
       U201(isNatural(N), N, X, activate(XS))
     , tail(cons(N, XS)) -> U211(isNatural(N), activate(XS))
     , take(N, XS) -> U221(isNatural(N), N, XS)
     , natsFrom(X) -> n__natsFrom(X)
     , s(X) -> n__s(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)
     , 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(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__nil()) -> nil()
     , activate(n__afterNth(X1, X2)) ->
       afterNth(activate(X1), activate(X2))
     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
     , activate(n__fst(X)) -> fst(activate(X))
     , activate(n__snd(X)) -> snd(activate(X))
     , activate(n__tail(X)) -> tail(activate(X))
     , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
     , activate(n__0()) -> 0()
     , activate(n__head(X)) -> head(activate(X))
     , activate(n__sel(X1, X2)) -> sel(activate(X1), activate(X2))
     , activate(n__pair(X1, X2)) -> pair(activate(X1), activate(X2))
     , activate(n__splitAt(X1, X2)) ->
       splitAt(activate(X1), activate(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 nokinds-noand FR

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES nokinds-noand FR

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  U101(tt(), V2) -> U102(isLNat(activate(V2)))
     , U102(tt()) -> tt()
     , U11(tt(), N, XS) ->
       U12(isLNat(activate(XS)), activate(N), activate(XS))
     , U111(tt()) -> tt()
     , U12(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS)))
     , U121(tt()) -> tt()
     , U131(tt(), V2) -> U132(isLNat(activate(V2)))
     , U132(tt()) -> tt()
     , U141(tt(), V2) -> U142(isLNat(activate(V2)))
     , U142(tt()) -> tt()
     , U151(tt(), V2) -> U152(isLNat(activate(V2)))
     , U152(tt()) -> tt()
     , U161(tt(), N) ->
       cons(activate(N), n__natsFrom(n__s(activate(N))))
     , U171(tt(), N, XS) ->
       U172(isLNat(activate(XS)), activate(N), activate(XS))
     , U172(tt(), N, XS) -> head(afterNth(activate(N), activate(XS)))
     , U181(tt(), Y) -> U182(isLNat(activate(Y)), activate(Y))
     , U182(tt(), Y) -> activate(Y)
     , U191(tt(), XS) -> pair(nil(), activate(XS))
     , U201(tt(), N, X, XS) ->
       U202(isNatural(activate(X)),
            activate(N),
            activate(X),
            activate(XS))
     , U202(tt(), N, X, XS) ->
       U203(isLNat(activate(XS)), activate(N), activate(X), activate(XS))
     , U203(tt(), N, X, XS) ->
       U204(splitAt(activate(N), activate(XS)), activate(X))
     , U204(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
     , U21(tt(), X, Y) -> U22(isLNat(activate(Y)), activate(X))
     , U211(tt(), XS) -> U212(isLNat(activate(XS)), activate(XS))
     , U212(tt(), XS) -> activate(XS)
     , U22(tt(), X) -> activate(X)
     , U221(tt(), N, XS) ->
       U222(isLNat(activate(XS)), activate(N), activate(XS))
     , U222(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS)))
     , U31(tt(), N, XS) -> U32(isLNat(activate(XS)), activate(N))
     , U32(tt(), N) -> activate(N)
     , U41(tt(), V2) -> U42(isLNat(activate(V2)))
     , U42(tt()) -> tt()
     , U51(tt(), V2) -> U52(isLNat(activate(V2)))
     , U52(tt()) -> tt()
     , U61(tt()) -> tt()
     , U71(tt()) -> tt()
     , U81(tt()) -> tt()
     , U91(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(isNatural(activate(V1)), activate(V2))
     , isLNat(n__cons(V1, V2)) ->
       U51(isNatural(activate(V1)), activate(V2))
     , isLNat(n__fst(V1)) -> U61(isPLNat(activate(V1)))
     , isLNat(n__natsFrom(V1)) -> U71(isNatural(activate(V1)))
     , isLNat(n__snd(V1)) -> U81(isPLNat(activate(V1)))
     , isLNat(n__tail(V1)) -> U91(isLNat(activate(V1)))
     , isLNat(n__take(V1, V2)) ->
       U101(isNatural(activate(V1)), activate(V2))
     , isNatural(n__0()) -> tt()
     , isNatural(n__head(V1)) -> U111(isLNat(activate(V1)))
     , isNatural(n__s(V1)) -> U121(isNatural(activate(V1)))
     , isNatural(n__sel(V1, V2)) ->
       U131(isNatural(activate(V1)), activate(V2))
     , isPLNat(n__pair(V1, V2)) ->
       U141(isLNat(activate(V1)), activate(V2))
     , isPLNat(n__splitAt(V1, V2)) ->
       U151(isNatural(activate(V1)), activate(V2))
     , natsFrom(N) -> U161(isNatural(N), N)
     , sel(N, XS) -> U171(isNatural(N), N, XS)
     , snd(pair(X, Y)) -> U181(isLNat(X), Y)
     , splitAt(0(), XS) -> U191(isLNat(XS), XS)
     , splitAt(s(N), cons(X, XS)) ->
       U201(isNatural(N), N, X, activate(XS))
     , tail(cons(N, XS)) -> U211(isNatural(N), activate(XS))
     , take(N, XS) -> U221(isNatural(N), N, XS)
     , natsFrom(X) -> n__natsFrom(X)
     , s(X) -> n__s(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)
     , 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(activate(X))
     , activate(n__s(X)) -> s(activate(X))
     , activate(n__nil()) -> nil()
     , activate(n__afterNth(X1, X2)) ->
       afterNth(activate(X1), activate(X2))
     , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
     , activate(n__fst(X)) -> fst(activate(X))
     , activate(n__snd(X)) -> snd(activate(X))
     , activate(n__tail(X)) -> tail(activate(X))
     , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
     , activate(n__0()) -> 0()
     , activate(n__head(X)) -> head(activate(X))
     , activate(n__sel(X1, X2)) -> sel(activate(X1), activate(X2))
     , activate(n__pair(X1, X2)) -> pair(activate(X1), activate(X2))
     , activate(n__splitAt(X1, X2)) ->
       splitAt(activate(X1), activate(X2))
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds