LMPO

Execution Time (secs)	0.220
Answer	MAYBE
Input	Transformed CSR 04 ExSec4 2 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__natsFrom(N) -> cons(mark(N), natsFrom(s(N)))
     , a__fst(pair(XS, YS)) -> mark(XS)
     , a__snd(pair(XS, YS)) -> mark(YS)
     , a__splitAt(0(), XS) -> pair(nil(), mark(XS))
     , a__splitAt(s(N), cons(X, XS)) ->
       a__u(a__splitAt(mark(N), mark(XS)), N, X, XS)
     , a__u(pair(YS, ZS), N, X, XS) -> pair(cons(mark(X), YS), mark(ZS))
     , a__head(cons(N, XS)) -> mark(N)
     , a__tail(cons(N, XS)) -> mark(XS)
     , a__sel(N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
     , a__take(N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
     , a__afterNth(N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
     , mark(natsFrom(X)) -> a__natsFrom(mark(X))
     , mark(fst(X)) -> a__fst(mark(X))
     , mark(snd(X)) -> a__snd(mark(X))
     , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
     , mark(u(X1, X2, X3, X4)) -> a__u(mark(X1), X2, X3, X4)
     , mark(head(X)) -> a__head(mark(X))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__natsFrom(X) -> natsFrom(X)
     , a__fst(X) -> fst(X)
     , a__snd(X) -> snd(X)
     , a__splitAt(X1, X2) -> splitAt(X1, X2)
     , a__u(X1, X2, X3, X4) -> u(X1, X2, X3, X4)
     , a__head(X) -> head(X)
     , a__tail(X) -> tail(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__afterNth(X1, X2) -> afterNth(X1, X2)
     , a__take(X1, X2) -> take(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.605
Answer	MAYBE
Input	Transformed CSR 04 ExSec4 2 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__natsFrom(N) -> cons(mark(N), natsFrom(s(N)))
     , a__fst(pair(XS, YS)) -> mark(XS)
     , a__snd(pair(XS, YS)) -> mark(YS)
     , a__splitAt(0(), XS) -> pair(nil(), mark(XS))
     , a__splitAt(s(N), cons(X, XS)) ->
       a__u(a__splitAt(mark(N), mark(XS)), N, X, XS)
     , a__u(pair(YS, ZS), N, X, XS) -> pair(cons(mark(X), YS), mark(ZS))
     , a__head(cons(N, XS)) -> mark(N)
     , a__tail(cons(N, XS)) -> mark(XS)
     , a__sel(N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
     , a__take(N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
     , a__afterNth(N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
     , mark(natsFrom(X)) -> a__natsFrom(mark(X))
     , mark(fst(X)) -> a__fst(mark(X))
     , mark(snd(X)) -> a__snd(mark(X))
     , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
     , mark(u(X1, X2, X3, X4)) -> a__u(mark(X1), X2, X3, X4)
     , mark(head(X)) -> a__head(mark(X))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__natsFrom(X) -> natsFrom(X)
     , a__fst(X) -> fst(X)
     , a__snd(X) -> snd(X)
     , a__splitAt(X1, X2) -> splitAt(X1, X2)
     , a__u(X1, X2, X3, X4) -> u(X1, X2, X3, X4)
     , a__head(X) -> head(X)
     , a__tail(X) -> tail(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__afterNth(X1, X2) -> afterNth(X1, X2)
     , a__take(X1, X2) -> take(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.191
Answer	MAYBE
Input	Transformed CSR 04 ExSec4 2 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__natsFrom(N) -> cons(mark(N), natsFrom(s(N)))
     , a__fst(pair(XS, YS)) -> mark(XS)
     , a__snd(pair(XS, YS)) -> mark(YS)
     , a__splitAt(0(), XS) -> pair(nil(), mark(XS))
     , a__splitAt(s(N), cons(X, XS)) ->
       a__u(a__splitAt(mark(N), mark(XS)), N, X, XS)
     , a__u(pair(YS, ZS), N, X, XS) -> pair(cons(mark(X), YS), mark(ZS))
     , a__head(cons(N, XS)) -> mark(N)
     , a__tail(cons(N, XS)) -> mark(XS)
     , a__sel(N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
     , a__take(N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
     , a__afterNth(N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
     , mark(natsFrom(X)) -> a__natsFrom(mark(X))
     , mark(fst(X)) -> a__fst(mark(X))
     , mark(snd(X)) -> a__snd(mark(X))
     , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
     , mark(u(X1, X2, X3, X4)) -> a__u(mark(X1), X2, X3, X4)
     , mark(head(X)) -> a__head(mark(X))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__natsFrom(X) -> natsFrom(X)
     , a__fst(X) -> fst(X)
     , a__snd(X) -> snd(X)
     , a__splitAt(X1, X2) -> splitAt(X1, X2)
     , a__u(X1, X2, X3, X4) -> u(X1, X2, X3, X4)
     , a__head(X) -> head(X)
     , a__tail(X) -> tail(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__afterNth(X1, X2) -> afterNth(X1, X2)
     , a__take(X1, X2) -> take(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.183
Answer	MAYBE
Input	Transformed CSR 04 ExSec4 2 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__natsFrom(N) -> cons(mark(N), natsFrom(s(N)))
     , a__fst(pair(XS, YS)) -> mark(XS)
     , a__snd(pair(XS, YS)) -> mark(YS)
     , a__splitAt(0(), XS) -> pair(nil(), mark(XS))
     , a__splitAt(s(N), cons(X, XS)) ->
       a__u(a__splitAt(mark(N), mark(XS)), N, X, XS)
     , a__u(pair(YS, ZS), N, X, XS) -> pair(cons(mark(X), YS), mark(ZS))
     , a__head(cons(N, XS)) -> mark(N)
     , a__tail(cons(N, XS)) -> mark(XS)
     , a__sel(N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
     , a__take(N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
     , a__afterNth(N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
     , mark(natsFrom(X)) -> a__natsFrom(mark(X))
     , mark(fst(X)) -> a__fst(mark(X))
     , mark(snd(X)) -> a__snd(mark(X))
     , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
     , mark(u(X1, X2, X3, X4)) -> a__u(mark(X1), X2, X3, X4)
     , mark(head(X)) -> a__head(mark(X))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__natsFrom(X) -> natsFrom(X)
     , a__fst(X) -> fst(X)
     , a__snd(X) -> snd(X)
     , a__splitAt(X1, X2) -> splitAt(X1, X2)
     , a__u(X1, X2, X3, X4) -> u(X1, X2, X3, X4)
     , a__head(X) -> head(X)
     , a__tail(X) -> tail(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__afterNth(X1, X2) -> afterNth(X1, X2)
     , a__take(X1, X2) -> take(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.167
Answer	MAYBE
Input	Transformed CSR 04 ExSec4 2 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__natsFrom(N) -> cons(mark(N), natsFrom(s(N)))
     , a__fst(pair(XS, YS)) -> mark(XS)
     , a__snd(pair(XS, YS)) -> mark(YS)
     , a__splitAt(0(), XS) -> pair(nil(), mark(XS))
     , a__splitAt(s(N), cons(X, XS)) ->
       a__u(a__splitAt(mark(N), mark(XS)), N, X, XS)
     , a__u(pair(YS, ZS), N, X, XS) -> pair(cons(mark(X), YS), mark(ZS))
     , a__head(cons(N, XS)) -> mark(N)
     , a__tail(cons(N, XS)) -> mark(XS)
     , a__sel(N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
     , a__take(N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
     , a__afterNth(N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
     , mark(natsFrom(X)) -> a__natsFrom(mark(X))
     , mark(fst(X)) -> a__fst(mark(X))
     , mark(snd(X)) -> a__snd(mark(X))
     , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
     , mark(u(X1, X2, X3, X4)) -> a__u(mark(X1), X2, X3, X4)
     , mark(head(X)) -> a__head(mark(X))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__natsFrom(X) -> natsFrom(X)
     , a__fst(X) -> fst(X)
     , a__snd(X) -> snd(X)
     , a__splitAt(X1, X2) -> splitAt(X1, X2)
     , a__u(X1, X2, X3, X4) -> u(X1, X2, X3, X4)
     , a__head(X) -> head(X)
     , a__tail(X) -> tail(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__afterNth(X1, X2) -> afterNth(X1, X2)
     , a__take(X1, X2) -> take(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.184
Answer	MAYBE
Input	Transformed CSR 04 ExSec4 2 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__natsFrom(N) -> cons(mark(N), natsFrom(s(N)))
     , a__fst(pair(XS, YS)) -> mark(XS)
     , a__snd(pair(XS, YS)) -> mark(YS)
     , a__splitAt(0(), XS) -> pair(nil(), mark(XS))
     , a__splitAt(s(N), cons(X, XS)) ->
       a__u(a__splitAt(mark(N), mark(XS)), N, X, XS)
     , a__u(pair(YS, ZS), N, X, XS) -> pair(cons(mark(X), YS), mark(ZS))
     , a__head(cons(N, XS)) -> mark(N)
     , a__tail(cons(N, XS)) -> mark(XS)
     , a__sel(N, XS) -> a__head(a__afterNth(mark(N), mark(XS)))
     , a__take(N, XS) -> a__fst(a__splitAt(mark(N), mark(XS)))
     , a__afterNth(N, XS) -> a__snd(a__splitAt(mark(N), mark(XS)))
     , mark(natsFrom(X)) -> a__natsFrom(mark(X))
     , mark(fst(X)) -> a__fst(mark(X))
     , mark(snd(X)) -> a__snd(mark(X))
     , mark(splitAt(X1, X2)) -> a__splitAt(mark(X1), mark(X2))
     , mark(u(X1, X2, X3, X4)) -> a__u(mark(X1), X2, X3, X4)
     , mark(head(X)) -> a__head(mark(X))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(afterNth(X1, X2)) -> a__afterNth(mark(X1), mark(X2))
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__natsFrom(X) -> natsFrom(X)
     , a__fst(X) -> fst(X)
     , a__snd(X) -> snd(X)
     , a__splitAt(X1, X2) -> splitAt(X1, X2)
     , a__u(X1, X2, X3, X4) -> u(X1, X2, X3, X4)
     , a__head(X) -> head(X)
     , a__tail(X) -> tail(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__afterNth(X1, X2) -> afterNth(X1, X2)
     , a__take(X1, X2) -> take(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 ExSec4 2 DLMMU04 GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)