LMPO

Execution Time (secs)	0.769
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nosorts-noand Z

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.838
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nosorts-noand Z

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.786
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nosorts-noand Z

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.556
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nosorts-noand Z

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.613
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nosorts-noand Z

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.743
Answer	MAYBE
Input	Transformed CSR 04 LISTUTILITIES nosorts-noand Z

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 LISTUTILITIES nosorts-noand Z

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)