LMPO

Execution Time (secs)	0.166
Answer	MAYBE
Input	Transformed CSR 04 ExSec11 1 Luc02a GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
     , a__sqr(0()) -> 0()
     , a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)), a__dbl(mark(X))))
     , a__dbl(0()) -> 0()
     , a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , a__half(0()) -> 0()
     , a__half(s(0())) -> 0()
     , a__half(s(s(X))) -> s(a__half(mark(X)))
     , a__half(dbl(X)) -> mark(X)
     , mark(terms(X)) -> a__terms(mark(X))
     , mark(sqr(X)) -> a__sqr(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(dbl(X)) -> a__dbl(mark(X))
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(half(X)) -> a__half(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(recip(X)) -> recip(mark(X))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__terms(X) -> terms(X)
     , a__sqr(X) -> sqr(X)
     , a__add(X1, X2) -> add(X1, X2)
     , a__dbl(X) -> dbl(X)
     , a__first(X1, X2) -> first(X1, X2)
     , a__half(X) -> half(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.216
Answer	MAYBE
Input	Transformed CSR 04 ExSec11 1 Luc02a GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
     , a__sqr(0()) -> 0()
     , a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)), a__dbl(mark(X))))
     , a__dbl(0()) -> 0()
     , a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , a__half(0()) -> 0()
     , a__half(s(0())) -> 0()
     , a__half(s(s(X))) -> s(a__half(mark(X)))
     , a__half(dbl(X)) -> mark(X)
     , mark(terms(X)) -> a__terms(mark(X))
     , mark(sqr(X)) -> a__sqr(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(dbl(X)) -> a__dbl(mark(X))
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(half(X)) -> a__half(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(recip(X)) -> recip(mark(X))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__terms(X) -> terms(X)
     , a__sqr(X) -> sqr(X)
     , a__add(X1, X2) -> add(X1, X2)
     , a__dbl(X) -> dbl(X)
     , a__first(X1, X2) -> first(X1, X2)
     , a__half(X) -> half(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.168
Answer	MAYBE
Input	Transformed CSR 04 ExSec11 1 Luc02a GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
     , a__sqr(0()) -> 0()
     , a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)), a__dbl(mark(X))))
     , a__dbl(0()) -> 0()
     , a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , a__half(0()) -> 0()
     , a__half(s(0())) -> 0()
     , a__half(s(s(X))) -> s(a__half(mark(X)))
     , a__half(dbl(X)) -> mark(X)
     , mark(terms(X)) -> a__terms(mark(X))
     , mark(sqr(X)) -> a__sqr(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(dbl(X)) -> a__dbl(mark(X))
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(half(X)) -> a__half(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(recip(X)) -> recip(mark(X))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__terms(X) -> terms(X)
     , a__sqr(X) -> sqr(X)
     , a__add(X1, X2) -> add(X1, X2)
     , a__dbl(X) -> dbl(X)
     , a__first(X1, X2) -> first(X1, X2)
     , a__half(X) -> half(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.121
Answer	MAYBE
Input	Transformed CSR 04 ExSec11 1 Luc02a GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
     , a__sqr(0()) -> 0()
     , a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)), a__dbl(mark(X))))
     , a__dbl(0()) -> 0()
     , a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , a__half(0()) -> 0()
     , a__half(s(0())) -> 0()
     , a__half(s(s(X))) -> s(a__half(mark(X)))
     , a__half(dbl(X)) -> mark(X)
     , mark(terms(X)) -> a__terms(mark(X))
     , mark(sqr(X)) -> a__sqr(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(dbl(X)) -> a__dbl(mark(X))
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(half(X)) -> a__half(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(recip(X)) -> recip(mark(X))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__terms(X) -> terms(X)
     , a__sqr(X) -> sqr(X)
     , a__add(X1, X2) -> add(X1, X2)
     , a__dbl(X) -> dbl(X)
     , a__first(X1, X2) -> first(X1, X2)
     , a__half(X) -> half(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.213
Answer	MAYBE
Input	Transformed CSR 04 ExSec11 1 Luc02a GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
     , a__sqr(0()) -> 0()
     , a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)), a__dbl(mark(X))))
     , a__dbl(0()) -> 0()
     , a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , a__half(0()) -> 0()
     , a__half(s(0())) -> 0()
     , a__half(s(s(X))) -> s(a__half(mark(X)))
     , a__half(dbl(X)) -> mark(X)
     , mark(terms(X)) -> a__terms(mark(X))
     , mark(sqr(X)) -> a__sqr(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(dbl(X)) -> a__dbl(mark(X))
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(half(X)) -> a__half(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(recip(X)) -> recip(mark(X))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__terms(X) -> terms(X)
     , a__sqr(X) -> sqr(X)
     , a__add(X1, X2) -> add(X1, X2)
     , a__dbl(X) -> dbl(X)
     , a__first(X1, X2) -> first(X1, X2)
     , a__half(X) -> half(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.237
Answer	MAYBE
Input	Transformed CSR 04 ExSec11 1 Luc02a GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__terms(N) -> cons(recip(a__sqr(mark(N))), terms(s(N)))
     , a__sqr(0()) -> 0()
     , a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)), a__dbl(mark(X))))
     , a__dbl(0()) -> 0()
     , a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__first(0(), X) -> nil()
     , a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z))
     , a__half(0()) -> 0()
     , a__half(s(0())) -> 0()
     , a__half(s(s(X))) -> s(a__half(mark(X)))
     , a__half(dbl(X)) -> mark(X)
     , mark(terms(X)) -> a__terms(mark(X))
     , mark(sqr(X)) -> a__sqr(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(dbl(X)) -> a__dbl(mark(X))
     , mark(first(X1, X2)) -> a__first(mark(X1), mark(X2))
     , mark(half(X)) -> a__half(mark(X))
     , mark(cons(X1, X2)) -> cons(mark(X1), X2)
     , mark(recip(X)) -> recip(mark(X))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(nil()) -> nil()
     , a__terms(X) -> terms(X)
     , a__sqr(X) -> sqr(X)
     , a__add(X1, X2) -> add(X1, X2)
     , a__dbl(X) -> dbl(X)
     , a__first(X1, X2) -> first(X1, X2)
     , a__half(X) -> half(X)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 ExSec11 1 Luc02a GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)