Problem Transformed CSR 04 LISTUTILITIES complete GM

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES complete GM

stdout:

MAYBE

Problem:
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)

Proof:
Open

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES complete GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  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)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES complete GM

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 LISTUTILITIES complete GM

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  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)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds