Problem Maude 06 LISTUTILITIES complete

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Maude 06 LISTUTILITIES complete

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Maude 06 LISTUTILITIES complete

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  U101(tt(), V1, V2) -> U102(isNatural(V1), V2)
     , U102(tt(), V2) -> U103(isLNat(V2))
     , U103(tt()) -> tt()
     , U11(tt(), N, XS) -> snd(splitAt(N, XS))
     , U111(tt(), V1) -> U112(isLNat(V1))
     , U112(tt()) -> tt()
     , U121(tt(), V1) -> U122(isNatural(V1))
     , U122(tt()) -> tt()
     , U131(tt(), V1, V2) -> U132(isNatural(V1), V2)
     , U132(tt(), V2) -> U133(isLNat(V2))
     , U133(tt()) -> tt()
     , U141(tt(), V1, V2) -> U142(isLNat(V1), V2)
     , U142(tt(), V2) -> U143(isLNat(V2))
     , U143(tt()) -> tt()
     , U151(tt(), V1, V2) -> U152(isNatural(V1), V2)
     , U152(tt(), V2) -> U153(isLNat(V2))
     , U153(tt()) -> tt()
     , U161(tt(), N) -> cons(N, natsFrom(s(N)))
     , U171(tt(), N, XS) -> head(afterNth(N, XS))
     , U181(tt(), Y) -> Y
     , U191(tt(), XS) -> pair(nil(), XS)
     , U201(tt(), N, X, XS) -> U202(splitAt(N, XS), X)
     , U202(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
     , U21(tt(), X) -> X
     , U211(tt(), XS) -> XS
     , U221(tt(), N, XS) -> fst(splitAt(N, XS))
     , U31(tt(), N) -> N
     , U41(tt(), V1, V2) -> U42(isNatural(V1), V2)
     , U42(tt(), V2) -> U43(isLNat(V2))
     , U43(tt()) -> tt()
     , U51(tt(), V1, V2) -> U52(isNatural(V1), V2)
     , U52(tt(), V2) -> U53(isLNat(V2))
     , U53(tt()) -> tt()
     , U61(tt(), V1) -> U62(isPLNat(V1))
     , U62(tt()) -> tt()
     , U71(tt(), V1) -> U72(isNatural(V1))
     , U72(tt()) -> tt()
     , U81(tt(), V1) -> U82(isPLNat(V1))
     , U82(tt()) -> tt()
     , U91(tt(), V1) -> U92(isLNat(V1))
     , U92(tt()) -> tt()
     , afterNth(N, XS) ->
       U11(and(and(isNatural(N), isNaturalKind(N)),
               and(isLNat(XS), isLNatKind(XS))),
           N,
           XS)
     , and(tt(), X) -> X
     , fst(pair(X, Y)) ->
       U21(and(and(isLNat(X), isLNatKind(X)),
               and(isLNat(Y), isLNatKind(Y))),
           X)
     , head(cons(N, XS)) ->
       U31(and(and(isNatural(N), isNaturalKind(N)),
               and(isLNat(XS), isLNatKind(XS))),
           N)
     , isLNat(nil()) -> tt()
     , isLNat(afterNth(V1, V2)) ->
       U41(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isLNat(cons(V1, V2)) ->
       U51(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isLNat(fst(V1)) -> U61(isPLNatKind(V1), V1)
     , isLNat(natsFrom(V1)) -> U71(isNaturalKind(V1), V1)
     , isLNat(snd(V1)) -> U81(isPLNatKind(V1), V1)
     , isLNat(tail(V1)) -> U91(isLNatKind(V1), V1)
     , isLNat(take(V1, V2)) ->
       U101(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isLNatKind(nil()) -> tt()
     , isLNatKind(afterNth(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , isLNatKind(cons(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , isLNatKind(fst(V1)) -> isPLNatKind(V1)
     , isLNatKind(natsFrom(V1)) -> isNaturalKind(V1)
     , isLNatKind(snd(V1)) -> isPLNatKind(V1)
     , isLNatKind(tail(V1)) -> isLNatKind(V1)
     , isLNatKind(take(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , isNatural(0()) -> tt()
     , isNatural(head(V1)) -> U111(isLNatKind(V1), V1)
     , isNatural(s(V1)) -> U121(isNaturalKind(V1), V1)
     , isNatural(sel(V1, V2)) ->
       U131(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isNaturalKind(0()) -> tt()
     , isNaturalKind(head(V1)) -> isLNatKind(V1)
     , isNaturalKind(s(V1)) -> isNaturalKind(V1)
     , isNaturalKind(sel(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , isPLNat(pair(V1, V2)) ->
       U141(and(isLNatKind(V1), isLNatKind(V2)), V1, V2)
     , isPLNat(splitAt(V1, V2)) ->
       U151(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isPLNatKind(pair(V1, V2)) -> and(isLNatKind(V1), isLNatKind(V2))
     , isPLNatKind(splitAt(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , natsFrom(N) -> U161(and(isNatural(N), isNaturalKind(N)), N)
     , sel(N, XS) ->
       U171(and(and(isNatural(N), isNaturalKind(N)),
                and(isLNat(XS), isLNatKind(XS))),
            N,
            XS)
     , snd(pair(X, Y)) ->
       U181(and(and(isLNat(X), isLNatKind(X)),
                and(isLNat(Y), isLNatKind(Y))),
            Y)
     , splitAt(0(), XS) -> U191(and(isLNat(XS), isLNatKind(XS)), XS)
     , splitAt(s(N), cons(X, XS)) ->
       U201(and(and(isNatural(N), isNaturalKind(N)),
                and(and(isNatural(X), isNaturalKind(X)),
                    and(isLNat(XS), isLNatKind(XS)))),
            N,
            X,
            XS)
     , tail(cons(N, XS)) ->
       U211(and(and(isNatural(N), isNaturalKind(N)),
                and(isLNat(XS), isLNatKind(XS))),
            XS)
     , take(N, XS) ->
       U221(and(and(isNatural(N), isNaturalKind(N)),
                and(isLNat(XS), isLNatKind(XS))),
            N,
            XS)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Maude 06 LISTUTILITIES complete

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Maude 06 LISTUTILITIES complete

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  U101(tt(), V1, V2) -> U102(isNatural(V1), V2)
     , U102(tt(), V2) -> U103(isLNat(V2))
     , U103(tt()) -> tt()
     , U11(tt(), N, XS) -> snd(splitAt(N, XS))
     , U111(tt(), V1) -> U112(isLNat(V1))
     , U112(tt()) -> tt()
     , U121(tt(), V1) -> U122(isNatural(V1))
     , U122(tt()) -> tt()
     , U131(tt(), V1, V2) -> U132(isNatural(V1), V2)
     , U132(tt(), V2) -> U133(isLNat(V2))
     , U133(tt()) -> tt()
     , U141(tt(), V1, V2) -> U142(isLNat(V1), V2)
     , U142(tt(), V2) -> U143(isLNat(V2))
     , U143(tt()) -> tt()
     , U151(tt(), V1, V2) -> U152(isNatural(V1), V2)
     , U152(tt(), V2) -> U153(isLNat(V2))
     , U153(tt()) -> tt()
     , U161(tt(), N) -> cons(N, natsFrom(s(N)))
     , U171(tt(), N, XS) -> head(afterNth(N, XS))
     , U181(tt(), Y) -> Y
     , U191(tt(), XS) -> pair(nil(), XS)
     , U201(tt(), N, X, XS) -> U202(splitAt(N, XS), X)
     , U202(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
     , U21(tt(), X) -> X
     , U211(tt(), XS) -> XS
     , U221(tt(), N, XS) -> fst(splitAt(N, XS))
     , U31(tt(), N) -> N
     , U41(tt(), V1, V2) -> U42(isNatural(V1), V2)
     , U42(tt(), V2) -> U43(isLNat(V2))
     , U43(tt()) -> tt()
     , U51(tt(), V1, V2) -> U52(isNatural(V1), V2)
     , U52(tt(), V2) -> U53(isLNat(V2))
     , U53(tt()) -> tt()
     , U61(tt(), V1) -> U62(isPLNat(V1))
     , U62(tt()) -> tt()
     , U71(tt(), V1) -> U72(isNatural(V1))
     , U72(tt()) -> tt()
     , U81(tt(), V1) -> U82(isPLNat(V1))
     , U82(tt()) -> tt()
     , U91(tt(), V1) -> U92(isLNat(V1))
     , U92(tt()) -> tt()
     , afterNth(N, XS) ->
       U11(and(and(isNatural(N), isNaturalKind(N)),
               and(isLNat(XS), isLNatKind(XS))),
           N,
           XS)
     , and(tt(), X) -> X
     , fst(pair(X, Y)) ->
       U21(and(and(isLNat(X), isLNatKind(X)),
               and(isLNat(Y), isLNatKind(Y))),
           X)
     , head(cons(N, XS)) ->
       U31(and(and(isNatural(N), isNaturalKind(N)),
               and(isLNat(XS), isLNatKind(XS))),
           N)
     , isLNat(nil()) -> tt()
     , isLNat(afterNth(V1, V2)) ->
       U41(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isLNat(cons(V1, V2)) ->
       U51(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isLNat(fst(V1)) -> U61(isPLNatKind(V1), V1)
     , isLNat(natsFrom(V1)) -> U71(isNaturalKind(V1), V1)
     , isLNat(snd(V1)) -> U81(isPLNatKind(V1), V1)
     , isLNat(tail(V1)) -> U91(isLNatKind(V1), V1)
     , isLNat(take(V1, V2)) ->
       U101(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isLNatKind(nil()) -> tt()
     , isLNatKind(afterNth(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , isLNatKind(cons(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , isLNatKind(fst(V1)) -> isPLNatKind(V1)
     , isLNatKind(natsFrom(V1)) -> isNaturalKind(V1)
     , isLNatKind(snd(V1)) -> isPLNatKind(V1)
     , isLNatKind(tail(V1)) -> isLNatKind(V1)
     , isLNatKind(take(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , isNatural(0()) -> tt()
     , isNatural(head(V1)) -> U111(isLNatKind(V1), V1)
     , isNatural(s(V1)) -> U121(isNaturalKind(V1), V1)
     , isNatural(sel(V1, V2)) ->
       U131(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isNaturalKind(0()) -> tt()
     , isNaturalKind(head(V1)) -> isLNatKind(V1)
     , isNaturalKind(s(V1)) -> isNaturalKind(V1)
     , isNaturalKind(sel(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , isPLNat(pair(V1, V2)) ->
       U141(and(isLNatKind(V1), isLNatKind(V2)), V1, V2)
     , isPLNat(splitAt(V1, V2)) ->
       U151(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
     , isPLNatKind(pair(V1, V2)) -> and(isLNatKind(V1), isLNatKind(V2))
     , isPLNatKind(splitAt(V1, V2)) ->
       and(isNaturalKind(V1), isLNatKind(V2))
     , natsFrom(N) -> U161(and(isNatural(N), isNaturalKind(N)), N)
     , sel(N, XS) ->
       U171(and(and(isNatural(N), isNaturalKind(N)),
                and(isLNat(XS), isLNatKind(XS))),
            N,
            XS)
     , snd(pair(X, Y)) ->
       U181(and(and(isLNat(X), isLNatKind(X)),
                and(isLNat(Y), isLNatKind(Y))),
            Y)
     , splitAt(0(), XS) -> U191(and(isLNat(XS), isLNatKind(XS)), XS)
     , splitAt(s(N), cons(X, XS)) ->
       U201(and(and(isNatural(N), isNaturalKind(N)),
                and(and(isNatural(X), isNaturalKind(X)),
                    and(isLNat(XS), isLNatKind(XS)))),
            N,
            X,
            XS)
     , tail(cons(N, XS)) ->
       U211(and(and(isNatural(N), isNaturalKind(N)),
                and(isLNat(XS), isLNatKind(XS))),
            XS)
     , take(N, XS) ->
       U221(and(and(isNatural(N), isNaturalKind(N)),
                and(isLNat(XS), isLNatKind(XS))),
            N,
            XS)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds