LMPO

Execution Time (secs)	0.219
Answer	MAYBE
Input	Transformed CSR 04 Ex4 7 37 Bor03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__sel(0(), cons(X, XS)) -> mark(X)
     , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
     , a__minus(X, 0()) -> 0()
     , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
     , a__quot(0(), s(Y)) -> 0()
     , a__quot(s(X), s(Y)) ->
       s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
     , a__zWquot(XS, nil()) -> nil()
     , a__zWquot(nil(), XS) -> nil()
     , a__zWquot(cons(X, XS), cons(Y, YS)) ->
       cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
     , mark(from(X)) -> a__from(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
     , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
     , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__from(X) -> from(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__minus(X1, X2) -> minus(X1, X2)
     , a__quot(X1, X2) -> quot(X1, X2)
     , a__zWquot(X1, X2) -> zWquot(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.227
Answer	MAYBE
Input	Transformed CSR 04 Ex4 7 37 Bor03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__sel(0(), cons(X, XS)) -> mark(X)
     , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
     , a__minus(X, 0()) -> 0()
     , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
     , a__quot(0(), s(Y)) -> 0()
     , a__quot(s(X), s(Y)) ->
       s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
     , a__zWquot(XS, nil()) -> nil()
     , a__zWquot(nil(), XS) -> nil()
     , a__zWquot(cons(X, XS), cons(Y, YS)) ->
       cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
     , mark(from(X)) -> a__from(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
     , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
     , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__from(X) -> from(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__minus(X1, X2) -> minus(X1, X2)
     , a__quot(X1, X2) -> quot(X1, X2)
     , a__zWquot(X1, X2) -> zWquot(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.138
Answer	MAYBE
Input	Transformed CSR 04 Ex4 7 37 Bor03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__sel(0(), cons(X, XS)) -> mark(X)
     , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
     , a__minus(X, 0()) -> 0()
     , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
     , a__quot(0(), s(Y)) -> 0()
     , a__quot(s(X), s(Y)) ->
       s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
     , a__zWquot(XS, nil()) -> nil()
     , a__zWquot(nil(), XS) -> nil()
     , a__zWquot(cons(X, XS), cons(Y, YS)) ->
       cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
     , mark(from(X)) -> a__from(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
     , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
     , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__from(X) -> from(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__minus(X1, X2) -> minus(X1, X2)
     , a__quot(X1, X2) -> quot(X1, X2)
     , a__zWquot(X1, X2) -> zWquot(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.128
Answer	MAYBE
Input	Transformed CSR 04 Ex4 7 37 Bor03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__sel(0(), cons(X, XS)) -> mark(X)
     , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
     , a__minus(X, 0()) -> 0()
     , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
     , a__quot(0(), s(Y)) -> 0()
     , a__quot(s(X), s(Y)) ->
       s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
     , a__zWquot(XS, nil()) -> nil()
     , a__zWquot(nil(), XS) -> nil()
     , a__zWquot(cons(X, XS), cons(Y, YS)) ->
       cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
     , mark(from(X)) -> a__from(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
     , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
     , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__from(X) -> from(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__minus(X1, X2) -> minus(X1, X2)
     , a__quot(X1, X2) -> quot(X1, X2)
     , a__zWquot(X1, X2) -> zWquot(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.222
Answer	MAYBE
Input	Transformed CSR 04 Ex4 7 37 Bor03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__sel(0(), cons(X, XS)) -> mark(X)
     , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
     , a__minus(X, 0()) -> 0()
     , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
     , a__quot(0(), s(Y)) -> 0()
     , a__quot(s(X), s(Y)) ->
       s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
     , a__zWquot(XS, nil()) -> nil()
     , a__zWquot(nil(), XS) -> nil()
     , a__zWquot(cons(X, XS), cons(Y, YS)) ->
       cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
     , mark(from(X)) -> a__from(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
     , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
     , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__from(X) -> from(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__minus(X1, X2) -> minus(X1, X2)
     , a__quot(X1, X2) -> quot(X1, X2)
     , a__zWquot(X1, X2) -> zWquot(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.160
Answer	MAYBE
Input	Transformed CSR 04 Ex4 7 37 Bor03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__sel(0(), cons(X, XS)) -> mark(X)
     , a__sel(s(N), cons(X, XS)) -> a__sel(mark(N), mark(XS))
     , a__minus(X, 0()) -> 0()
     , a__minus(s(X), s(Y)) -> a__minus(mark(X), mark(Y))
     , a__quot(0(), s(Y)) -> 0()
     , a__quot(s(X), s(Y)) ->
       s(a__quot(a__minus(mark(X), mark(Y)), s(mark(Y))))
     , a__zWquot(XS, nil()) -> nil()
     , a__zWquot(nil(), XS) -> nil()
     , a__zWquot(cons(X, XS), cons(Y, YS)) ->
       cons(a__quot(mark(X), mark(Y)), zWquot(XS, YS))
     , mark(from(X)) -> a__from(mark(X))
     , mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2))
     , mark(minus(X1, X2)) -> a__minus(mark(X1), mark(X2))
     , mark(quot(X1, X2)) -> a__quot(mark(X1), mark(X2))
     , mark(zWquot(X1, X2)) -> a__zWquot(mark(X1), mark(X2))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__from(X) -> from(X)
     , a__sel(X1, X2) -> sel(X1, X2)
     , a__minus(X1, X2) -> minus(X1, X2)
     , a__quot(X1, X2) -> quot(X1, X2)
     , a__zWquot(X1, X2) -> zWquot(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 Ex4 7 37 Bor03 GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)