LMPO

Execution Time (secs)	0.171
Answer	MAYBE
Input	Transformed CSR 04 Ex5 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__pairNs() -> cons(0(), incr(oddNs()))
     , a__oddNs() -> a__incr(a__pairNs())
     , a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
     , a__take(0(), XS) -> nil()
     , a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
     , a__zip(nil(), XS) -> nil()
     , a__zip(X, nil()) -> nil()
     , a__zip(cons(X, XS), cons(Y, YS)) ->
       cons(pair(mark(X), mark(Y)), zip(XS, YS))
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__repItems(nil()) -> nil()
     , a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
     , mark(pairNs()) -> a__pairNs()
     , mark(incr(X)) -> a__incr(mark(X))
     , mark(oddNs()) -> a__oddNs()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(repItems(X)) -> a__repItems(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , a__pairNs() -> pairNs()
     , a__incr(X) -> incr(X)
     , a__oddNs() -> oddNs()
     , a__take(X1, X2) -> take(X1, X2)
     , a__zip(X1, X2) -> zip(X1, X2)
     , a__tail(X) -> tail(X)
     , a__repItems(X) -> repItems(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.267
Answer	MAYBE
Input	Transformed CSR 04 Ex5 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__pairNs() -> cons(0(), incr(oddNs()))
     , a__oddNs() -> a__incr(a__pairNs())
     , a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
     , a__take(0(), XS) -> nil()
     , a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
     , a__zip(nil(), XS) -> nil()
     , a__zip(X, nil()) -> nil()
     , a__zip(cons(X, XS), cons(Y, YS)) ->
       cons(pair(mark(X), mark(Y)), zip(XS, YS))
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__repItems(nil()) -> nil()
     , a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
     , mark(pairNs()) -> a__pairNs()
     , mark(incr(X)) -> a__incr(mark(X))
     , mark(oddNs()) -> a__oddNs()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(repItems(X)) -> a__repItems(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , a__pairNs() -> pairNs()
     , a__incr(X) -> incr(X)
     , a__oddNs() -> oddNs()
     , a__take(X1, X2) -> take(X1, X2)
     , a__zip(X1, X2) -> zip(X1, X2)
     , a__tail(X) -> tail(X)
     , a__repItems(X) -> repItems(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.156
Answer	MAYBE
Input	Transformed CSR 04 Ex5 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__pairNs() -> cons(0(), incr(oddNs()))
     , a__oddNs() -> a__incr(a__pairNs())
     , a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
     , a__take(0(), XS) -> nil()
     , a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
     , a__zip(nil(), XS) -> nil()
     , a__zip(X, nil()) -> nil()
     , a__zip(cons(X, XS), cons(Y, YS)) ->
       cons(pair(mark(X), mark(Y)), zip(XS, YS))
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__repItems(nil()) -> nil()
     , a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
     , mark(pairNs()) -> a__pairNs()
     , mark(incr(X)) -> a__incr(mark(X))
     , mark(oddNs()) -> a__oddNs()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(repItems(X)) -> a__repItems(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , a__pairNs() -> pairNs()
     , a__incr(X) -> incr(X)
     , a__oddNs() -> oddNs()
     , a__take(X1, X2) -> take(X1, X2)
     , a__zip(X1, X2) -> zip(X1, X2)
     , a__tail(X) -> tail(X)
     , a__repItems(X) -> repItems(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.137
Answer	MAYBE
Input	Transformed CSR 04 Ex5 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__pairNs() -> cons(0(), incr(oddNs()))
     , a__oddNs() -> a__incr(a__pairNs())
     , a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
     , a__take(0(), XS) -> nil()
     , a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
     , a__zip(nil(), XS) -> nil()
     , a__zip(X, nil()) -> nil()
     , a__zip(cons(X, XS), cons(Y, YS)) ->
       cons(pair(mark(X), mark(Y)), zip(XS, YS))
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__repItems(nil()) -> nil()
     , a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
     , mark(pairNs()) -> a__pairNs()
     , mark(incr(X)) -> a__incr(mark(X))
     , mark(oddNs()) -> a__oddNs()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(repItems(X)) -> a__repItems(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , a__pairNs() -> pairNs()
     , a__incr(X) -> incr(X)
     , a__oddNs() -> oddNs()
     , a__take(X1, X2) -> take(X1, X2)
     , a__zip(X1, X2) -> zip(X1, X2)
     , a__tail(X) -> tail(X)
     , a__repItems(X) -> repItems(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.126
Answer	MAYBE
Input	Transformed CSR 04 Ex5 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__pairNs() -> cons(0(), incr(oddNs()))
     , a__oddNs() -> a__incr(a__pairNs())
     , a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
     , a__take(0(), XS) -> nil()
     , a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
     , a__zip(nil(), XS) -> nil()
     , a__zip(X, nil()) -> nil()
     , a__zip(cons(X, XS), cons(Y, YS)) ->
       cons(pair(mark(X), mark(Y)), zip(XS, YS))
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__repItems(nil()) -> nil()
     , a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
     , mark(pairNs()) -> a__pairNs()
     , mark(incr(X)) -> a__incr(mark(X))
     , mark(oddNs()) -> a__oddNs()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(repItems(X)) -> a__repItems(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , a__pairNs() -> pairNs()
     , a__incr(X) -> incr(X)
     , a__oddNs() -> oddNs()
     , a__take(X1, X2) -> take(X1, X2)
     , a__zip(X1, X2) -> zip(X1, X2)
     , a__tail(X) -> tail(X)
     , a__repItems(X) -> repItems(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.124
Answer	MAYBE
Input	Transformed CSR 04 Ex5 DLMMU04 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__pairNs() -> cons(0(), incr(oddNs()))
     , a__oddNs() -> a__incr(a__pairNs())
     , a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS))
     , a__take(0(), XS) -> nil()
     , a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS))
     , a__zip(nil(), XS) -> nil()
     , a__zip(X, nil()) -> nil()
     , a__zip(cons(X, XS), cons(Y, YS)) ->
       cons(pair(mark(X), mark(Y)), zip(XS, YS))
     , a__tail(cons(X, XS)) -> mark(XS)
     , a__repItems(nil()) -> nil()
     , a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS)))
     , mark(pairNs()) -> a__pairNs()
     , mark(incr(X)) -> a__incr(mark(X))
     , mark(oddNs()) -> a__oddNs()
     , mark(take(X1, X2)) -> a__take(mark(X1), mark(X2))
     , mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2))
     , mark(tail(X)) -> a__tail(mark(X))
     , mark(repItems(X)) -> a__repItems(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(nil()) -> nil()
     , mark(pair(X1, X2)) -> pair(mark(X1), mark(X2))
     , a__pairNs() -> pairNs()
     , a__incr(X) -> incr(X)
     , a__oddNs() -> oddNs()
     , a__take(X1, X2) -> take(X1, X2)
     , a__zip(X1, X2) -> zip(X1, X2)
     , a__tail(X) -> tail(X)
     , a__repItems(X) -> repItems(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 Ex5 DLMMU04 GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)