LMPO

Execution Time (secs)	0.203
Answer	MAYBE
Input	Transformed CSR 04 Ex1 2 AEL03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__2ndspos(0(), Z) -> rnil()
     , a__2ndspos(s(N), cons(X, cons(Y, Z))) ->
       rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
     , a__2ndsneg(0(), Z) -> rnil()
     , a__2ndsneg(s(N), cons(X, cons(Y, Z))) ->
       rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
     , a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
     , a__plus(0(), Y) -> mark(Y)
     , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
     , a__times(0(), Y) -> 0()
     , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
     , a__square(X) -> a__times(mark(X), mark(X))
     , mark(from(X)) -> a__from(mark(X))
     , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
     , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
     , mark(pi(X)) -> a__pi(mark(X))
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
     , mark(square(X)) -> a__square(mark(X))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(posrecip(X)) -> posrecip(mark(X))
     , mark(negrecip(X)) -> negrecip(mark(X))
     , mark(nil()) -> nil()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(rnil()) -> rnil()
     , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
     , a__from(X) -> from(X)
     , a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
     , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
     , a__pi(X) -> pi(X)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__times(X1, X2) -> times(X1, X2)
     , a__square(X) -> square(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.417
Answer	MAYBE
Input	Transformed CSR 04 Ex1 2 AEL03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__2ndspos(0(), Z) -> rnil()
     , a__2ndspos(s(N), cons(X, cons(Y, Z))) ->
       rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
     , a__2ndsneg(0(), Z) -> rnil()
     , a__2ndsneg(s(N), cons(X, cons(Y, Z))) ->
       rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
     , a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
     , a__plus(0(), Y) -> mark(Y)
     , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
     , a__times(0(), Y) -> 0()
     , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
     , a__square(X) -> a__times(mark(X), mark(X))
     , mark(from(X)) -> a__from(mark(X))
     , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
     , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
     , mark(pi(X)) -> a__pi(mark(X))
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
     , mark(square(X)) -> a__square(mark(X))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(posrecip(X)) -> posrecip(mark(X))
     , mark(negrecip(X)) -> negrecip(mark(X))
     , mark(nil()) -> nil()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(rnil()) -> rnil()
     , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
     , a__from(X) -> from(X)
     , a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
     , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
     , a__pi(X) -> pi(X)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__times(X1, X2) -> times(X1, X2)
     , a__square(X) -> square(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.288
Answer	MAYBE
Input	Transformed CSR 04 Ex1 2 AEL03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__2ndspos(0(), Z) -> rnil()
     , a__2ndspos(s(N), cons(X, cons(Y, Z))) ->
       rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
     , a__2ndsneg(0(), Z) -> rnil()
     , a__2ndsneg(s(N), cons(X, cons(Y, Z))) ->
       rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
     , a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
     , a__plus(0(), Y) -> mark(Y)
     , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
     , a__times(0(), Y) -> 0()
     , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
     , a__square(X) -> a__times(mark(X), mark(X))
     , mark(from(X)) -> a__from(mark(X))
     , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
     , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
     , mark(pi(X)) -> a__pi(mark(X))
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
     , mark(square(X)) -> a__square(mark(X))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(posrecip(X)) -> posrecip(mark(X))
     , mark(negrecip(X)) -> negrecip(mark(X))
     , mark(nil()) -> nil()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(rnil()) -> rnil()
     , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
     , a__from(X) -> from(X)
     , a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
     , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
     , a__pi(X) -> pi(X)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__times(X1, X2) -> times(X1, X2)
     , a__square(X) -> square(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.270
Answer	MAYBE
Input	Transformed CSR 04 Ex1 2 AEL03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__2ndspos(0(), Z) -> rnil()
     , a__2ndspos(s(N), cons(X, cons(Y, Z))) ->
       rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
     , a__2ndsneg(0(), Z) -> rnil()
     , a__2ndsneg(s(N), cons(X, cons(Y, Z))) ->
       rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
     , a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
     , a__plus(0(), Y) -> mark(Y)
     , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
     , a__times(0(), Y) -> 0()
     , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
     , a__square(X) -> a__times(mark(X), mark(X))
     , mark(from(X)) -> a__from(mark(X))
     , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
     , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
     , mark(pi(X)) -> a__pi(mark(X))
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
     , mark(square(X)) -> a__square(mark(X))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(posrecip(X)) -> posrecip(mark(X))
     , mark(negrecip(X)) -> negrecip(mark(X))
     , mark(nil()) -> nil()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(rnil()) -> rnil()
     , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
     , a__from(X) -> from(X)
     , a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
     , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
     , a__pi(X) -> pi(X)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__times(X1, X2) -> times(X1, X2)
     , a__square(X) -> square(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.210
Answer	MAYBE
Input	Transformed CSR 04 Ex1 2 AEL03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__2ndspos(0(), Z) -> rnil()
     , a__2ndspos(s(N), cons(X, cons(Y, Z))) ->
       rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
     , a__2ndsneg(0(), Z) -> rnil()
     , a__2ndsneg(s(N), cons(X, cons(Y, Z))) ->
       rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
     , a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
     , a__plus(0(), Y) -> mark(Y)
     , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
     , a__times(0(), Y) -> 0()
     , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
     , a__square(X) -> a__times(mark(X), mark(X))
     , mark(from(X)) -> a__from(mark(X))
     , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
     , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
     , mark(pi(X)) -> a__pi(mark(X))
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
     , mark(square(X)) -> a__square(mark(X))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(posrecip(X)) -> posrecip(mark(X))
     , mark(negrecip(X)) -> negrecip(mark(X))
     , mark(nil()) -> nil()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(rnil()) -> rnil()
     , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
     , a__from(X) -> from(X)
     , a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
     , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
     , a__pi(X) -> pi(X)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__times(X1, X2) -> times(X1, X2)
     , a__square(X) -> square(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.201
Answer	MAYBE
Input	Transformed CSR 04 Ex1 2 AEL03 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__from(X) -> cons(mark(X), from(s(X)))
     , a__2ndspos(0(), Z) -> rnil()
     , a__2ndspos(s(N), cons(X, cons(Y, Z))) ->
       rcons(posrecip(mark(Y)), a__2ndsneg(mark(N), mark(Z)))
     , a__2ndsneg(0(), Z) -> rnil()
     , a__2ndsneg(s(N), cons(X, cons(Y, Z))) ->
       rcons(negrecip(mark(Y)), a__2ndspos(mark(N), mark(Z)))
     , a__pi(X) -> a__2ndspos(mark(X), a__from(0()))
     , a__plus(0(), Y) -> mark(Y)
     , a__plus(s(X), Y) -> s(a__plus(mark(X), mark(Y)))
     , a__times(0(), Y) -> 0()
     , a__times(s(X), Y) -> a__plus(mark(Y), a__times(mark(X), mark(Y)))
     , a__square(X) -> a__times(mark(X), mark(X))
     , mark(from(X)) -> a__from(mark(X))
     , mark(2ndspos(X1, X2)) -> a__2ndspos(mark(X1), mark(X2))
     , mark(2ndsneg(X1, X2)) -> a__2ndsneg(mark(X1), mark(X2))
     , mark(pi(X)) -> a__pi(mark(X))
     , mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
     , mark(times(X1, X2)) -> a__times(mark(X1), mark(X2))
     , mark(square(X)) -> a__square(mark(X))
     , mark(0()) -> 0()
     , mark(s(X)) -> s(mark(X))
     , mark(posrecip(X)) -> posrecip(mark(X))
     , mark(negrecip(X)) -> negrecip(mark(X))
     , mark(nil()) -> nil()
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(rnil()) -> rnil()
     , mark(rcons(X1, X2)) -> rcons(mark(X1), mark(X2))
     , a__from(X) -> from(X)
     , a__2ndspos(X1, X2) -> 2ndspos(X1, X2)
     , a__2ndsneg(X1, X2) -> 2ndsneg(X1, X2)
     , a__pi(X) -> pi(X)
     , a__plus(X1, X2) -> plus(X1, X2)
     , a__times(X1, X2) -> times(X1, X2)
     , a__square(X) -> square(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 Ex1 2 AEL03 GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)