LMPO

Execution Time (secs)	0.117
Answer	MAYBE
Input	CSR 04 ExAppendixB AEL03

MAYBE

We consider the following Problem:

  Strict Trs:
    {  from(X) -> cons(X, from(s(X)))
     , 2ndspos(0(), Z) -> rnil()
     , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z))
     , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
       rcons(posrecip(Y), 2ndsneg(N, Z))
     , 2ndsneg(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z))
     , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
       rcons(negrecip(Y), 2ndspos(N, Z))
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(0(), Y) -> Y
     , plus(s(X), Y) -> s(plus(X, Y))
     , times(0(), Y) -> 0()
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , square(X) -> times(X, X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.153
Answer	MAYBE
Input	CSR 04 ExAppendixB AEL03

MAYBE

We consider the following Problem:

  Strict Trs:
    {  from(X) -> cons(X, from(s(X)))
     , 2ndspos(0(), Z) -> rnil()
     , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z))
     , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
       rcons(posrecip(Y), 2ndsneg(N, Z))
     , 2ndsneg(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z))
     , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
       rcons(negrecip(Y), 2ndspos(N, Z))
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(0(), Y) -> Y
     , plus(s(X), Y) -> s(plus(X, Y))
     , times(0(), Y) -> 0()
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , square(X) -> times(X, X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.118
Answer	MAYBE
Input	CSR 04 ExAppendixB AEL03

MAYBE

We consider the following Problem:

  Strict Trs:
    {  from(X) -> cons(X, from(s(X)))
     , 2ndspos(0(), Z) -> rnil()
     , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z))
     , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
       rcons(posrecip(Y), 2ndsneg(N, Z))
     , 2ndsneg(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z))
     , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
       rcons(negrecip(Y), 2ndspos(N, Z))
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(0(), Y) -> Y
     , plus(s(X), Y) -> s(plus(X, Y))
     , times(0(), Y) -> 0()
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , square(X) -> times(X, X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.127
Answer	MAYBE
Input	CSR 04 ExAppendixB AEL03

MAYBE

We consider the following Problem:

  Strict Trs:
    {  from(X) -> cons(X, from(s(X)))
     , 2ndspos(0(), Z) -> rnil()
     , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z))
     , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
       rcons(posrecip(Y), 2ndsneg(N, Z))
     , 2ndsneg(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z))
     , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
       rcons(negrecip(Y), 2ndspos(N, Z))
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(0(), Y) -> Y
     , plus(s(X), Y) -> s(plus(X, Y))
     , times(0(), Y) -> 0()
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , square(X) -> times(X, X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.097
Answer	MAYBE
Input	CSR 04 ExAppendixB AEL03

MAYBE

We consider the following Problem:

  Strict Trs:
    {  from(X) -> cons(X, from(s(X)))
     , 2ndspos(0(), Z) -> rnil()
     , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z))
     , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
       rcons(posrecip(Y), 2ndsneg(N, Z))
     , 2ndsneg(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z))
     , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
       rcons(negrecip(Y), 2ndspos(N, Z))
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(0(), Y) -> Y
     , plus(s(X), Y) -> s(plus(X, Y))
     , times(0(), Y) -> 0()
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , square(X) -> times(X, X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.179
Answer	MAYBE
Input	CSR 04 ExAppendixB AEL03

MAYBE

We consider the following Problem:

  Strict Trs:
    {  from(X) -> cons(X, from(s(X)))
     , 2ndspos(0(), Z) -> rnil()
     , 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, Z))
     , 2ndspos(s(N), cons2(X, cons(Y, Z))) ->
       rcons(posrecip(Y), 2ndsneg(N, Z))
     , 2ndsneg(0(), Z) -> rnil()
     , 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, Z))
     , 2ndsneg(s(N), cons2(X, cons(Y, Z))) ->
       rcons(negrecip(Y), 2ndspos(N, Z))
     , pi(X) -> 2ndspos(X, from(0()))
     , plus(0(), Y) -> Y
     , plus(s(X), Y) -> s(plus(X, Y))
     , times(0(), Y) -> 0()
     , times(s(X), Y) -> plus(Y, times(X, Y))
     , square(X) -> times(X, X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem CSR 04 ExAppendixB AEL03

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)