LMPO

Execution Time (secs)	0.447
Answer	MAYBE
Input	Maude 06 LISTUTILITIES nosorts-noand

MAYBE

We consider the following Problem:

  Strict Trs:
    {  U11(tt(), N, XS) -> U12(tt(), N, XS)
     , U12(tt(), N, XS) -> snd(splitAt(N, XS))
     , U21(tt(), X) -> U22(tt(), X)
     , U22(tt(), X) -> X
     , U31(tt(), N) -> U32(tt(), N)
     , U32(tt(), N) -> N
     , U41(tt(), N, XS) -> U42(tt(), N, XS)
     , U42(tt(), N, XS) -> head(afterNth(N, XS))
     , U51(tt(), Y) -> U52(tt(), Y)
     , U52(tt(), Y) -> Y
     , U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
     , U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
     , U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
     , U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
     , U71(tt(), XS) -> U72(tt(), XS)
     , U72(tt(), XS) -> XS
     , U81(tt(), N, XS) -> U82(tt(), N, XS)
     , U82(tt(), N, XS) -> fst(splitAt(N, XS))
     , afterNth(N, XS) -> U11(tt(), N, XS)
     , fst(pair(X, Y)) -> U21(tt(), X)
     , head(cons(N, XS)) -> U31(tt(), N)
     , natsFrom(N) -> cons(N, natsFrom(s(N)))
     , sel(N, XS) -> U41(tt(), N, XS)
     , snd(pair(X, Y)) -> U51(tt(), Y)
     , splitAt(0(), XS) -> pair(nil(), XS)
     , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
     , tail(cons(N, XS)) -> U71(tt(), XS)
     , take(N, XS) -> U81(tt(), N, XS)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.708
Answer	MAYBE
Input	Maude 06 LISTUTILITIES nosorts-noand

MAYBE

We consider the following Problem:

  Strict Trs:
    {  U11(tt(), N, XS) -> U12(tt(), N, XS)
     , U12(tt(), N, XS) -> snd(splitAt(N, XS))
     , U21(tt(), X) -> U22(tt(), X)
     , U22(tt(), X) -> X
     , U31(tt(), N) -> U32(tt(), N)
     , U32(tt(), N) -> N
     , U41(tt(), N, XS) -> U42(tt(), N, XS)
     , U42(tt(), N, XS) -> head(afterNth(N, XS))
     , U51(tt(), Y) -> U52(tt(), Y)
     , U52(tt(), Y) -> Y
     , U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
     , U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
     , U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
     , U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
     , U71(tt(), XS) -> U72(tt(), XS)
     , U72(tt(), XS) -> XS
     , U81(tt(), N, XS) -> U82(tt(), N, XS)
     , U82(tt(), N, XS) -> fst(splitAt(N, XS))
     , afterNth(N, XS) -> U11(tt(), N, XS)
     , fst(pair(X, Y)) -> U21(tt(), X)
     , head(cons(N, XS)) -> U31(tt(), N)
     , natsFrom(N) -> cons(N, natsFrom(s(N)))
     , sel(N, XS) -> U41(tt(), N, XS)
     , snd(pair(X, Y)) -> U51(tt(), Y)
     , splitAt(0(), XS) -> pair(nil(), XS)
     , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
     , tail(cons(N, XS)) -> U71(tt(), XS)
     , take(N, XS) -> U81(tt(), N, XS)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.489
Answer	MAYBE
Input	Maude 06 LISTUTILITIES nosorts-noand

MAYBE

We consider the following Problem:

  Strict Trs:
    {  U11(tt(), N, XS) -> U12(tt(), N, XS)
     , U12(tt(), N, XS) -> snd(splitAt(N, XS))
     , U21(tt(), X) -> U22(tt(), X)
     , U22(tt(), X) -> X
     , U31(tt(), N) -> U32(tt(), N)
     , U32(tt(), N) -> N
     , U41(tt(), N, XS) -> U42(tt(), N, XS)
     , U42(tt(), N, XS) -> head(afterNth(N, XS))
     , U51(tt(), Y) -> U52(tt(), Y)
     , U52(tt(), Y) -> Y
     , U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
     , U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
     , U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
     , U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
     , U71(tt(), XS) -> U72(tt(), XS)
     , U72(tt(), XS) -> XS
     , U81(tt(), N, XS) -> U82(tt(), N, XS)
     , U82(tt(), N, XS) -> fst(splitAt(N, XS))
     , afterNth(N, XS) -> U11(tt(), N, XS)
     , fst(pair(X, Y)) -> U21(tt(), X)
     , head(cons(N, XS)) -> U31(tt(), N)
     , natsFrom(N) -> cons(N, natsFrom(s(N)))
     , sel(N, XS) -> U41(tt(), N, XS)
     , snd(pair(X, Y)) -> U51(tt(), Y)
     , splitAt(0(), XS) -> pair(nil(), XS)
     , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
     , tail(cons(N, XS)) -> U71(tt(), XS)
     , take(N, XS) -> U81(tt(), N, XS)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.370
Answer	MAYBE
Input	Maude 06 LISTUTILITIES nosorts-noand

MAYBE

We consider the following Problem:

  Strict Trs:
    {  U11(tt(), N, XS) -> U12(tt(), N, XS)
     , U12(tt(), N, XS) -> snd(splitAt(N, XS))
     , U21(tt(), X) -> U22(tt(), X)
     , U22(tt(), X) -> X
     , U31(tt(), N) -> U32(tt(), N)
     , U32(tt(), N) -> N
     , U41(tt(), N, XS) -> U42(tt(), N, XS)
     , U42(tt(), N, XS) -> head(afterNth(N, XS))
     , U51(tt(), Y) -> U52(tt(), Y)
     , U52(tt(), Y) -> Y
     , U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
     , U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
     , U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
     , U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
     , U71(tt(), XS) -> U72(tt(), XS)
     , U72(tt(), XS) -> XS
     , U81(tt(), N, XS) -> U82(tt(), N, XS)
     , U82(tt(), N, XS) -> fst(splitAt(N, XS))
     , afterNth(N, XS) -> U11(tt(), N, XS)
     , fst(pair(X, Y)) -> U21(tt(), X)
     , head(cons(N, XS)) -> U31(tt(), N)
     , natsFrom(N) -> cons(N, natsFrom(s(N)))
     , sel(N, XS) -> U41(tt(), N, XS)
     , snd(pair(X, Y)) -> U51(tt(), Y)
     , splitAt(0(), XS) -> pair(nil(), XS)
     , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
     , tail(cons(N, XS)) -> U71(tt(), XS)
     , take(N, XS) -> U81(tt(), N, XS)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.371
Answer	MAYBE
Input	Maude 06 LISTUTILITIES nosorts-noand

MAYBE

We consider the following Problem:

  Strict Trs:
    {  U11(tt(), N, XS) -> U12(tt(), N, XS)
     , U12(tt(), N, XS) -> snd(splitAt(N, XS))
     , U21(tt(), X) -> U22(tt(), X)
     , U22(tt(), X) -> X
     , U31(tt(), N) -> U32(tt(), N)
     , U32(tt(), N) -> N
     , U41(tt(), N, XS) -> U42(tt(), N, XS)
     , U42(tt(), N, XS) -> head(afterNth(N, XS))
     , U51(tt(), Y) -> U52(tt(), Y)
     , U52(tt(), Y) -> Y
     , U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
     , U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
     , U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
     , U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
     , U71(tt(), XS) -> U72(tt(), XS)
     , U72(tt(), XS) -> XS
     , U81(tt(), N, XS) -> U82(tt(), N, XS)
     , U82(tt(), N, XS) -> fst(splitAt(N, XS))
     , afterNth(N, XS) -> U11(tt(), N, XS)
     , fst(pair(X, Y)) -> U21(tt(), X)
     , head(cons(N, XS)) -> U31(tt(), N)
     , natsFrom(N) -> cons(N, natsFrom(s(N)))
     , sel(N, XS) -> U41(tt(), N, XS)
     , snd(pair(X, Y)) -> U51(tt(), Y)
     , splitAt(0(), XS) -> pair(nil(), XS)
     , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
     , tail(cons(N, XS)) -> U71(tt(), XS)
     , take(N, XS) -> U81(tt(), N, XS)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.490
Answer	MAYBE
Input	Maude 06 LISTUTILITIES nosorts-noand

MAYBE

We consider the following Problem:

  Strict Trs:
    {  U11(tt(), N, XS) -> U12(tt(), N, XS)
     , U12(tt(), N, XS) -> snd(splitAt(N, XS))
     , U21(tt(), X) -> U22(tt(), X)
     , U22(tt(), X) -> X
     , U31(tt(), N) -> U32(tt(), N)
     , U32(tt(), N) -> N
     , U41(tt(), N, XS) -> U42(tt(), N, XS)
     , U42(tt(), N, XS) -> head(afterNth(N, XS))
     , U51(tt(), Y) -> U52(tt(), Y)
     , U52(tt(), Y) -> Y
     , U61(tt(), N, X, XS) -> U62(tt(), N, X, XS)
     , U62(tt(), N, X, XS) -> U63(tt(), N, X, XS)
     , U63(tt(), N, X, XS) -> U64(splitAt(N, XS), X)
     , U64(pair(YS, ZS), X) -> pair(cons(X, YS), ZS)
     , U71(tt(), XS) -> U72(tt(), XS)
     , U72(tt(), XS) -> XS
     , U81(tt(), N, XS) -> U82(tt(), N, XS)
     , U82(tt(), N, XS) -> fst(splitAt(N, XS))
     , afterNth(N, XS) -> U11(tt(), N, XS)
     , fst(pair(X, Y)) -> U21(tt(), X)
     , head(cons(N, XS)) -> U31(tt(), N)
     , natsFrom(N) -> cons(N, natsFrom(s(N)))
     , sel(N, XS) -> U41(tt(), N, XS)
     , snd(pair(X, Y)) -> U51(tt(), Y)
     , splitAt(0(), XS) -> pair(nil(), XS)
     , splitAt(s(N), cons(X, XS)) -> U61(tt(), N, X, XS)
     , tail(cons(N, XS)) -> U71(tt(), XS)
     , take(N, XS) -> U81(tt(), N, XS)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Maude 06 LISTUTILITIES nosorts-noand

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)