LMPO

Execution Time (secs)	0.230
Answer	MAYBE
Input	CiME 04 maude2

MAYBE

We consider the following Problem:

  Strict Trs:
    {  p(s(N)) -> N
     , +(N, 0()) -> N
     , +(s(N), s(M)) -> s(s(+(N, M)))
     , *(N, 0()) -> 0()
     , *(s(N), s(M)) -> s(+(N, +(M, *(N, M))))
     , gt(0(), M) -> False()
     , gt(NzN, 0()) -> u_4(is_NzNat(NzN))
     , u_4(True()) -> True()
     , is_NzNat(0()) -> False()
     , is_NzNat(s(N)) -> True()
     , gt(s(N), s(M)) -> gt(N, M)
     , lt(N, M) -> gt(M, N)
     , d(0(), N) -> N
     , d(s(N), s(M)) -> d(N, M)
     , quot(N, NzM) -> u_11(is_NzNat(NzM), N, NzM)
     , u_11(True(), N, NzM) -> u_1(gt(N, NzM), N, NzM)
     , u_1(True(), N, NzM) -> s(quot(d(N, NzM), NzM))
     , quot(NzM, NzM) -> u_01(is_NzNat(NzM))
     , u_01(True()) -> s(0())
     , quot(N, NzM) -> u_21(is_NzNat(NzM), NzM, N)
     , u_21(True(), NzM, N) -> u_2(gt(NzM, N))
     , u_2(True()) -> 0()
     , gcd(0(), N) -> 0()
     , gcd(NzM, NzM) -> u_02(is_NzNat(NzM), NzM)
     , u_02(True(), NzM) -> NzM
     , gcd(NzN, NzM) -> u_31(is_NzNat(NzN), is_NzNat(NzM), NzN, NzM)
     , u_31(True(), True(), NzN, NzM) -> u_3(gt(NzN, NzM), NzN, NzM)
     , u_3(True(), NzN, NzM) -> gcd(d(NzN, NzM), NzM)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.221
Answer	MAYBE
Input	CiME 04 maude2

MAYBE

We consider the following Problem:

  Strict Trs:
    {  p(s(N)) -> N
     , +(N, 0()) -> N
     , +(s(N), s(M)) -> s(s(+(N, M)))
     , *(N, 0()) -> 0()
     , *(s(N), s(M)) -> s(+(N, +(M, *(N, M))))
     , gt(0(), M) -> False()
     , gt(NzN, 0()) -> u_4(is_NzNat(NzN))
     , u_4(True()) -> True()
     , is_NzNat(0()) -> False()
     , is_NzNat(s(N)) -> True()
     , gt(s(N), s(M)) -> gt(N, M)
     , lt(N, M) -> gt(M, N)
     , d(0(), N) -> N
     , d(s(N), s(M)) -> d(N, M)
     , quot(N, NzM) -> u_11(is_NzNat(NzM), N, NzM)
     , u_11(True(), N, NzM) -> u_1(gt(N, NzM), N, NzM)
     , u_1(True(), N, NzM) -> s(quot(d(N, NzM), NzM))
     , quot(NzM, NzM) -> u_01(is_NzNat(NzM))
     , u_01(True()) -> s(0())
     , quot(N, NzM) -> u_21(is_NzNat(NzM), NzM, N)
     , u_21(True(), NzM, N) -> u_2(gt(NzM, N))
     , u_2(True()) -> 0()
     , gcd(0(), N) -> 0()
     , gcd(NzM, NzM) -> u_02(is_NzNat(NzM), NzM)
     , u_02(True(), NzM) -> NzM
     , gcd(NzN, NzM) -> u_31(is_NzNat(NzN), is_NzNat(NzM), NzN, NzM)
     , u_31(True(), True(), NzN, NzM) -> u_3(gt(NzN, NzM), NzN, NzM)
     , u_3(True(), NzN, NzM) -> gcd(d(NzN, NzM), NzM)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.259
Answer	MAYBE
Input	CiME 04 maude2

MAYBE

We consider the following Problem:

  Strict Trs:
    {  p(s(N)) -> N
     , +(N, 0()) -> N
     , +(s(N), s(M)) -> s(s(+(N, M)))
     , *(N, 0()) -> 0()
     , *(s(N), s(M)) -> s(+(N, +(M, *(N, M))))
     , gt(0(), M) -> False()
     , gt(NzN, 0()) -> u_4(is_NzNat(NzN))
     , u_4(True()) -> True()
     , is_NzNat(0()) -> False()
     , is_NzNat(s(N)) -> True()
     , gt(s(N), s(M)) -> gt(N, M)
     , lt(N, M) -> gt(M, N)
     , d(0(), N) -> N
     , d(s(N), s(M)) -> d(N, M)
     , quot(N, NzM) -> u_11(is_NzNat(NzM), N, NzM)
     , u_11(True(), N, NzM) -> u_1(gt(N, NzM), N, NzM)
     , u_1(True(), N, NzM) -> s(quot(d(N, NzM), NzM))
     , quot(NzM, NzM) -> u_01(is_NzNat(NzM))
     , u_01(True()) -> s(0())
     , quot(N, NzM) -> u_21(is_NzNat(NzM), NzM, N)
     , u_21(True(), NzM, N) -> u_2(gt(NzM, N))
     , u_2(True()) -> 0()
     , gcd(0(), N) -> 0()
     , gcd(NzM, NzM) -> u_02(is_NzNat(NzM), NzM)
     , u_02(True(), NzM) -> NzM
     , gcd(NzN, NzM) -> u_31(is_NzNat(NzN), is_NzNat(NzM), NzN, NzM)
     , u_31(True(), True(), NzN, NzM) -> u_3(gt(NzN, NzM), NzN, NzM)
     , u_3(True(), NzN, NzM) -> gcd(d(NzN, NzM), NzM)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.265
Answer	MAYBE
Input	CiME 04 maude2

MAYBE

We consider the following Problem:

  Strict Trs:
    {  p(s(N)) -> N
     , +(N, 0()) -> N
     , +(s(N), s(M)) -> s(s(+(N, M)))
     , *(N, 0()) -> 0()
     , *(s(N), s(M)) -> s(+(N, +(M, *(N, M))))
     , gt(0(), M) -> False()
     , gt(NzN, 0()) -> u_4(is_NzNat(NzN))
     , u_4(True()) -> True()
     , is_NzNat(0()) -> False()
     , is_NzNat(s(N)) -> True()
     , gt(s(N), s(M)) -> gt(N, M)
     , lt(N, M) -> gt(M, N)
     , d(0(), N) -> N
     , d(s(N), s(M)) -> d(N, M)
     , quot(N, NzM) -> u_11(is_NzNat(NzM), N, NzM)
     , u_11(True(), N, NzM) -> u_1(gt(N, NzM), N, NzM)
     , u_1(True(), N, NzM) -> s(quot(d(N, NzM), NzM))
     , quot(NzM, NzM) -> u_01(is_NzNat(NzM))
     , u_01(True()) -> s(0())
     , quot(N, NzM) -> u_21(is_NzNat(NzM), NzM, N)
     , u_21(True(), NzM, N) -> u_2(gt(NzM, N))
     , u_2(True()) -> 0()
     , gcd(0(), N) -> 0()
     , gcd(NzM, NzM) -> u_02(is_NzNat(NzM), NzM)
     , u_02(True(), NzM) -> NzM
     , gcd(NzN, NzM) -> u_31(is_NzNat(NzN), is_NzNat(NzM), NzN, NzM)
     , u_31(True(), True(), NzN, NzM) -> u_3(gt(NzN, NzM), NzN, NzM)
     , u_3(True(), NzN, NzM) -> gcd(d(NzN, NzM), NzM)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.225
Answer	MAYBE
Input	CiME 04 maude2

MAYBE

We consider the following Problem:

  Strict Trs:
    {  p(s(N)) -> N
     , +(N, 0()) -> N
     , +(s(N), s(M)) -> s(s(+(N, M)))
     , *(N, 0()) -> 0()
     , *(s(N), s(M)) -> s(+(N, +(M, *(N, M))))
     , gt(0(), M) -> False()
     , gt(NzN, 0()) -> u_4(is_NzNat(NzN))
     , u_4(True()) -> True()
     , is_NzNat(0()) -> False()
     , is_NzNat(s(N)) -> True()
     , gt(s(N), s(M)) -> gt(N, M)
     , lt(N, M) -> gt(M, N)
     , d(0(), N) -> N
     , d(s(N), s(M)) -> d(N, M)
     , quot(N, NzM) -> u_11(is_NzNat(NzM), N, NzM)
     , u_11(True(), N, NzM) -> u_1(gt(N, NzM), N, NzM)
     , u_1(True(), N, NzM) -> s(quot(d(N, NzM), NzM))
     , quot(NzM, NzM) -> u_01(is_NzNat(NzM))
     , u_01(True()) -> s(0())
     , quot(N, NzM) -> u_21(is_NzNat(NzM), NzM, N)
     , u_21(True(), NzM, N) -> u_2(gt(NzM, N))
     , u_2(True()) -> 0()
     , gcd(0(), N) -> 0()
     , gcd(NzM, NzM) -> u_02(is_NzNat(NzM), NzM)
     , u_02(True(), NzM) -> NzM
     , gcd(NzN, NzM) -> u_31(is_NzNat(NzN), is_NzNat(NzM), NzN, NzM)
     , u_31(True(), True(), NzN, NzM) -> u_3(gt(NzN, NzM), NzN, NzM)
     , u_3(True(), NzN, NzM) -> gcd(d(NzN, NzM), NzM)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.223
Answer	MAYBE
Input	CiME 04 maude2

MAYBE

We consider the following Problem:

  Strict Trs:
    {  p(s(N)) -> N
     , +(N, 0()) -> N
     , +(s(N), s(M)) -> s(s(+(N, M)))
     , *(N, 0()) -> 0()
     , *(s(N), s(M)) -> s(+(N, +(M, *(N, M))))
     , gt(0(), M) -> False()
     , gt(NzN, 0()) -> u_4(is_NzNat(NzN))
     , u_4(True()) -> True()
     , is_NzNat(0()) -> False()
     , is_NzNat(s(N)) -> True()
     , gt(s(N), s(M)) -> gt(N, M)
     , lt(N, M) -> gt(M, N)
     , d(0(), N) -> N
     , d(s(N), s(M)) -> d(N, M)
     , quot(N, NzM) -> u_11(is_NzNat(NzM), N, NzM)
     , u_11(True(), N, NzM) -> u_1(gt(N, NzM), N, NzM)
     , u_1(True(), N, NzM) -> s(quot(d(N, NzM), NzM))
     , quot(NzM, NzM) -> u_01(is_NzNat(NzM))
     , u_01(True()) -> s(0())
     , quot(N, NzM) -> u_21(is_NzNat(NzM), NzM, N)
     , u_21(True(), NzM, N) -> u_2(gt(NzM, N))
     , u_2(True()) -> 0()
     , gcd(0(), N) -> 0()
     , gcd(NzM, NzM) -> u_02(is_NzNat(NzM), NzM)
     , u_02(True(), NzM) -> NzM
     , gcd(NzN, NzM) -> u_31(is_NzNat(NzN), is_NzNat(NzM), NzN, NzM)
     , u_31(True(), True(), NzN, NzM) -> u_3(gt(NzN, NzM), NzN, NzM)
     , u_3(True(), NzN, NzM) -> gcd(d(NzN, NzM), NzM)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem CiME 04 maude2

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)