Problem Transformed CSR 04 LISTUTILITIES nokinds Z

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nokinds Z

stdout:

MAYBE

Problem:
U101(tt(),N,XS) -> fst(splitAt(activate(N),activate(XS)))
U11(tt(),N,XS) -> snd(splitAt(activate(N),activate(XS)))
U21(tt(),X) -> activate(X)
U31(tt(),N) -> activate(N)
U41(tt(),N) -> cons(activate(N),n__natsFrom(s(activate(N))))
U51(tt(),N,XS) -> head(afterNth(activate(N),activate(XS)))
U61(tt(),Y) -> activate(Y)
U71(tt(),XS) -> pair(nil(),activate(XS))
U81(tt(),N,X,XS) -> U82(splitAt(activate(N),activate(XS)),activate(X))
U82(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
U91(tt(),XS) -> activate(XS)
afterNth(N,XS) -> U11(and(isNatural(N),n__isLNat(XS)),N,XS)
and(tt(),X) -> activate(X)
fst(pair(X,Y)) -> U21(and(isLNat(X),n__isLNat(Y)),X)
head(cons(N,XS)) -> U31(and(isNatural(N),n__isLNat(activate(XS))),N)
isLNat(n__nil()) -> tt()
isLNat(n__afterNth(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2)))
isLNat(n__cons(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2)))
isLNat(n__fst(V1)) -> isPLNat(activate(V1))
isLNat(n__natsFrom(V1)) -> isNatural(activate(V1))
isLNat(n__snd(V1)) -> isPLNat(activate(V1))
isLNat(n__tail(V1)) -> isLNat(activate(V1))
isLNat(n__take(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2)))
isNatural(n__0()) -> tt()
isNatural(n__head(V1)) -> isLNat(activate(V1))
isNatural(n__s(V1)) -> isNatural(activate(V1))
isNatural(n__sel(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2)))
isPLNat(n__pair(V1,V2)) -> and(isLNat(activate(V1)),n__isLNat(activate(V2)))
isPLNat(n__splitAt(V1,V2)) -> and(isNatural(activate(V1)),n__isLNat(activate(V2)))
natsFrom(N) -> U41(isNatural(N),N)
sel(N,XS) -> U51(and(isNatural(N),n__isLNat(XS)),N,XS)
snd(pair(X,Y)) -> U61(and(isLNat(X),n__isLNat(Y)),Y)
splitAt(0(),XS) -> U71(isLNat(XS),XS)
splitAt(s(N),cons(X,XS)) ->
U81(and(isNatural(N),n__and(isNatural(X),n__isLNat(activate(XS)))),N,X,activate(XS))
tail(cons(N,XS)) -> U91(and(isNatural(N),n__isLNat(activate(XS))),activate(XS))
take(N,XS) -> U101(and(isNatural(N),n__isLNat(XS)),N,XS)
natsFrom(X) -> n__natsFrom(X)
isLNat(X) -> n__isLNat(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)
and(X1,X2) -> n__and(X1,X2)
activate(n__natsFrom(X)) -> natsFrom(X)
activate(n__isLNat(X)) -> isLNat(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(n__and(X1,X2)) -> and(X1,X2)
activate(X) -> X

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nokinds Z

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES nokinds Z

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  U101(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS)))
     , U11(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS)))
     , U21(tt(), X) -> activate(X)
     , U31(tt(), N) -> activate(N)
     , U41(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N))))
     , U51(tt(), N, XS) -> head(afterNth(activate(N), activate(XS)))
     , U61(tt(), Y) -> activate(Y)
     , U71(tt(), XS) -> pair(nil(), activate(XS))
     , U81(tt(), N, X, XS) ->
       U82(splitAt(activate(N), activate(XS)), activate(X))
     , U82(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
     , U91(tt(), XS) -> activate(XS)
     , afterNth(N, XS) -> U11(and(isNatural(N), n__isLNat(XS)), N, XS)
     , and(tt(), X) -> activate(X)
     , fst(pair(X, Y)) -> U21(and(isLNat(X), n__isLNat(Y)), X)
     , head(cons(N, XS)) ->
       U31(and(isNatural(N), n__isLNat(activate(XS))), N)
     , isLNat(n__nil()) -> tt()
     , isLNat(n__afterNth(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , isLNat(n__cons(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , isLNat(n__fst(V1)) -> isPLNat(activate(V1))
     , isLNat(n__natsFrom(V1)) -> isNatural(activate(V1))
     , isLNat(n__snd(V1)) -> isPLNat(activate(V1))
     , isLNat(n__tail(V1)) -> isLNat(activate(V1))
     , isLNat(n__take(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , isNatural(n__0()) -> tt()
     , isNatural(n__head(V1)) -> isLNat(activate(V1))
     , isNatural(n__s(V1)) -> isNatural(activate(V1))
     , isNatural(n__sel(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , isPLNat(n__pair(V1, V2)) ->
       and(isLNat(activate(V1)), n__isLNat(activate(V2)))
     , isPLNat(n__splitAt(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , natsFrom(N) -> U41(isNatural(N), N)
     , sel(N, XS) -> U51(and(isNatural(N), n__isLNat(XS)), N, XS)
     , snd(pair(X, Y)) -> U61(and(isLNat(X), n__isLNat(Y)), Y)
     , splitAt(0(), XS) -> U71(isLNat(XS), XS)
     , splitAt(s(N), cons(X, XS)) ->
       U81(and(isNatural(N),
               n__and(isNatural(X), n__isLNat(activate(XS)))),
           N,
           X,
           activate(XS))
     , tail(cons(N, XS)) ->
       U91(and(isNatural(N), n__isLNat(activate(XS))), activate(XS))
     , take(N, XS) -> U101(and(isNatural(N), n__isLNat(XS)), N, XS)
     , natsFrom(X) -> n__natsFrom(X)
     , isLNat(X) -> n__isLNat(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)
     , and(X1, X2) -> n__and(X1, X2)
     , activate(n__natsFrom(X)) -> natsFrom(X)
     , activate(n__isLNat(X)) -> isLNat(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(n__and(X1, X2)) -> and(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 nokinds Z

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES nokinds Z

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  U101(tt(), N, XS) -> fst(splitAt(activate(N), activate(XS)))
     , U11(tt(), N, XS) -> snd(splitAt(activate(N), activate(XS)))
     , U21(tt(), X) -> activate(X)
     , U31(tt(), N) -> activate(N)
     , U41(tt(), N) -> cons(activate(N), n__natsFrom(s(activate(N))))
     , U51(tt(), N, XS) -> head(afterNth(activate(N), activate(XS)))
     , U61(tt(), Y) -> activate(Y)
     , U71(tt(), XS) -> pair(nil(), activate(XS))
     , U81(tt(), N, X, XS) ->
       U82(splitAt(activate(N), activate(XS)), activate(X))
     , U82(pair(YS, ZS), X) -> pair(cons(activate(X), YS), ZS)
     , U91(tt(), XS) -> activate(XS)
     , afterNth(N, XS) -> U11(and(isNatural(N), n__isLNat(XS)), N, XS)
     , and(tt(), X) -> activate(X)
     , fst(pair(X, Y)) -> U21(and(isLNat(X), n__isLNat(Y)), X)
     , head(cons(N, XS)) ->
       U31(and(isNatural(N), n__isLNat(activate(XS))), N)
     , isLNat(n__nil()) -> tt()
     , isLNat(n__afterNth(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , isLNat(n__cons(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , isLNat(n__fst(V1)) -> isPLNat(activate(V1))
     , isLNat(n__natsFrom(V1)) -> isNatural(activate(V1))
     , isLNat(n__snd(V1)) -> isPLNat(activate(V1))
     , isLNat(n__tail(V1)) -> isLNat(activate(V1))
     , isLNat(n__take(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , isNatural(n__0()) -> tt()
     , isNatural(n__head(V1)) -> isLNat(activate(V1))
     , isNatural(n__s(V1)) -> isNatural(activate(V1))
     , isNatural(n__sel(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , isPLNat(n__pair(V1, V2)) ->
       and(isLNat(activate(V1)), n__isLNat(activate(V2)))
     , isPLNat(n__splitAt(V1, V2)) ->
       and(isNatural(activate(V1)), n__isLNat(activate(V2)))
     , natsFrom(N) -> U41(isNatural(N), N)
     , sel(N, XS) -> U51(and(isNatural(N), n__isLNat(XS)), N, XS)
     , snd(pair(X, Y)) -> U61(and(isLNat(X), n__isLNat(Y)), Y)
     , splitAt(0(), XS) -> U71(isLNat(XS), XS)
     , splitAt(s(N), cons(X, XS)) ->
       U81(and(isNatural(N),
               n__and(isNatural(X), n__isLNat(activate(XS)))),
           N,
           X,
           activate(XS))
     , tail(cons(N, XS)) ->
       U91(and(isNatural(N), n__isLNat(activate(XS))), activate(XS))
     , take(N, XS) -> U101(and(isNatural(N), n__isLNat(XS)), N, XS)
     , natsFrom(X) -> n__natsFrom(X)
     , isLNat(X) -> n__isLNat(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)
     , and(X1, X2) -> n__and(X1, X2)
     , activate(n__natsFrom(X)) -> natsFrom(X)
     , activate(n__isLNat(X)) -> isLNat(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(n__and(X1, X2)) -> and(X1, X2)
     , activate(X) -> X}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds