LMPO

Execution Time (secs)	0.093
Answer	MAYBE
Input	AG01 3.6b

MAYBE

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , gcd(0(), y) -> y
     , gcd(s(x), 0()) -> s(x)
     , gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
     , if_gcd(true(), s(x), s(y)) -> gcd(minus(x, y), s(y))
     , if_gcd(false(), s(x), s(y)) -> gcd(minus(y, x), s(x))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.095
Answer	MAYBE
Input	AG01 3.6b

MAYBE

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , gcd(0(), y) -> y
     , gcd(s(x), 0()) -> s(x)
     , gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
     , if_gcd(true(), s(x), s(y)) -> gcd(minus(x, y), s(y))
     , if_gcd(false(), s(x), s(y)) -> gcd(minus(y, x), s(x))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.112
Answer	MAYBE
Input	AG01 3.6b

MAYBE

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , gcd(0(), y) -> y
     , gcd(s(x), 0()) -> s(x)
     , gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
     , if_gcd(true(), s(x), s(y)) -> gcd(minus(x, y), s(y))
     , if_gcd(false(), s(x), s(y)) -> gcd(minus(y, x), s(x))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.084
Answer	MAYBE
Input	AG01 3.6b

MAYBE

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , gcd(0(), y) -> y
     , gcd(s(x), 0()) -> s(x)
     , gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
     , if_gcd(true(), s(x), s(y)) -> gcd(minus(x, y), s(y))
     , if_gcd(false(), s(x), s(y)) -> gcd(minus(y, x), s(x))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.082
Answer	MAYBE
Input	AG01 3.6b

MAYBE

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , gcd(0(), y) -> y
     , gcd(s(x), 0()) -> s(x)
     , gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
     , if_gcd(true(), s(x), s(y)) -> gcd(minus(x, y), s(y))
     , if_gcd(false(), s(x), s(y)) -> gcd(minus(y, x), s(x))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.087
Answer	MAYBE
Input	AG01 3.6b

MAYBE

We consider the following Problem:

  Strict Trs:
    {  le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(0(), y) -> 0()
     , minus(s(x), y) -> if_minus(le(s(x), y), s(x), y)
     , if_minus(true(), s(x), y) -> 0()
     , if_minus(false(), s(x), y) -> s(minus(x, y))
     , gcd(0(), y) -> y
     , gcd(s(x), 0()) -> s(x)
     , gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y))
     , if_gcd(true(), s(x), s(y)) -> gcd(minus(x, y), s(y))
     , if_gcd(false(), s(x), s(y)) -> gcd(minus(y, x), s(x))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem AG01 3.6b

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)