LMPO

Execution Time (secs)	0.045
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc02a L

MAYBE

We consider the following Problem:

  Strict Trs:
    {  terms(N) -> cons(recip(sqr(N)))
     , sqr(0()) -> 0()
     , sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , dbl(0()) -> 0()
     , dbl(s(X)) -> s(s(dbl(X)))
     , add(0(), X) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , first(0(), X) -> nil()
     , first(s(X), cons(Y)) -> cons(Y)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.154
Answer	YES(?,PRIMREC)
Input	Transformed CSR 04 Ex2 Luc02a L

YES(?,PRIMREC)

We consider the following Problem:

  Strict Trs:
    {  terms(N) -> cons(recip(sqr(N)))
     , sqr(0()) -> 0()
     , sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , dbl(0()) -> 0()
     , dbl(s(X)) -> s(s(dbl(X)))
     , add(0(), X) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , first(0(), X) -> nil()
     , first(s(X), cons(Y)) -> cons(Y)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,PRIMREC)

Proof:
  The input was oriented with the instance of
  'multiset path orders' as induced by the precedence

   terms > cons, terms > recip, terms > sqr, sqr > s, sqr > add,
   sqr > dbl, add > s, dbl > s, first > nil .

Hurray, we answered YES(?,PRIMREC)

POP*

Execution Time (secs)	0.043
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc02a L

MAYBE

We consider the following Problem:

  Strict Trs:
    {  terms(N) -> cons(recip(sqr(N)))
     , sqr(0()) -> 0()
     , sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , dbl(0()) -> 0()
     , dbl(s(X)) -> s(s(dbl(X)))
     , add(0(), X) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , first(0(), X) -> nil()
     , first(s(X), cons(Y)) -> cons(Y)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.089
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc02a L

MAYBE

We consider the following Problem:

  Strict Trs:
    {  terms(N) -> cons(recip(sqr(N)))
     , sqr(0()) -> 0()
     , sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , dbl(0()) -> 0()
     , dbl(s(X)) -> s(s(dbl(X)))
     , add(0(), X) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , first(0(), X) -> nil()
     , first(s(X), cons(Y)) -> cons(Y)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.044
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc02a L

MAYBE

We consider the following Problem:

  Strict Trs:
    {  terms(N) -> cons(recip(sqr(N)))
     , sqr(0()) -> 0()
     , sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , dbl(0()) -> 0()
     , dbl(s(X)) -> s(s(dbl(X)))
     , add(0(), X) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , first(0(), X) -> nil()
     , first(s(X), cons(Y)) -> cons(Y)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.069
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc02a L

MAYBE

We consider the following Problem:

  Strict Trs:
    {  terms(N) -> cons(recip(sqr(N)))
     , sqr(0()) -> 0()
     , sqr(s(X)) -> s(add(sqr(X), dbl(X)))
     , dbl(0()) -> 0()
     , dbl(s(X)) -> s(s(dbl(X)))
     , add(0(), X) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , first(0(), X) -> nil()
     , first(s(X), cons(Y)) -> cons(Y)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 Ex2 Luc02a L

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)