LMPO

Execution Time (secs)	0.130
Answer	MAYBE
Input	Transformed CSR 04 ExIntrod Zan97 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__fact(X) ->
       a__if(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__prod(0(), X) -> 0()
     , a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y)))
     , a__if(true(), X, Y) -> mark(X)
     , a__if(false(), X, Y) -> mark(Y)
     , a__zero(0()) -> true()
     , a__zero(s(X)) -> false()
     , a__p(s(X)) -> mark(X)
     , mark(fact(X)) -> a__fact(mark(X))
     , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
     , mark(zero(X)) -> a__zero(mark(X))
     , mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2))
     , mark(p(X)) -> a__p(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(true()) -> true()
     , mark(false()) -> false()
     , a__fact(X) -> fact(X)
     , a__if(X1, X2, X3) -> if(X1, X2, X3)
     , a__zero(X) -> zero(X)
     , a__prod(X1, X2) -> prod(X1, X2)
     , a__p(X) -> p(X)
     , a__add(X1, X2) -> add(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

MPO

Execution Time (secs)	0.192
Answer	MAYBE
Input	Transformed CSR 04 ExIntrod Zan97 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__fact(X) ->
       a__if(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__prod(0(), X) -> 0()
     , a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y)))
     , a__if(true(), X, Y) -> mark(X)
     , a__if(false(), X, Y) -> mark(Y)
     , a__zero(0()) -> true()
     , a__zero(s(X)) -> false()
     , a__p(s(X)) -> mark(X)
     , mark(fact(X)) -> a__fact(mark(X))
     , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
     , mark(zero(X)) -> a__zero(mark(X))
     , mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2))
     , mark(p(X)) -> a__p(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(true()) -> true()
     , mark(false()) -> false()
     , a__fact(X) -> fact(X)
     , a__if(X1, X2, X3) -> if(X1, X2, X3)
     , a__zero(X) -> zero(X)
     , a__prod(X1, X2) -> prod(X1, X2)
     , a__p(X) -> p(X)
     , a__add(X1, X2) -> add(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP*

Execution Time (secs)	0.191
Answer	MAYBE
Input	Transformed CSR 04 ExIntrod Zan97 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__fact(X) ->
       a__if(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__prod(0(), X) -> 0()
     , a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y)))
     , a__if(true(), X, Y) -> mark(X)
     , a__if(false(), X, Y) -> mark(Y)
     , a__zero(0()) -> true()
     , a__zero(s(X)) -> false()
     , a__p(s(X)) -> mark(X)
     , mark(fact(X)) -> a__fact(mark(X))
     , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
     , mark(zero(X)) -> a__zero(mark(X))
     , mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2))
     , mark(p(X)) -> a__p(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(true()) -> true()
     , mark(false()) -> false()
     , a__fact(X) -> fact(X)
     , a__if(X1, X2, X3) -> if(X1, X2, X3)
     , a__zero(X) -> zero(X)
     , a__prod(X1, X2) -> prod(X1, X2)
     , a__p(X) -> p(X)
     , a__add(X1, X2) -> add(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

POP* (PS)

Execution Time (secs)	0.171
Answer	MAYBE
Input	Transformed CSR 04 ExIntrod Zan97 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__fact(X) ->
       a__if(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__prod(0(), X) -> 0()
     , a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y)))
     , a__if(true(), X, Y) -> mark(X)
     , a__if(false(), X, Y) -> mark(Y)
     , a__zero(0()) -> true()
     , a__zero(s(X)) -> false()
     , a__p(s(X)) -> mark(X)
     , mark(fact(X)) -> a__fact(mark(X))
     , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
     , mark(zero(X)) -> a__zero(mark(X))
     , mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2))
     , mark(p(X)) -> a__p(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(true()) -> true()
     , mark(false()) -> false()
     , a__fact(X) -> fact(X)
     , a__if(X1, X2, X3) -> if(X1, X2, X3)
     , a__zero(X) -> zero(X)
     , a__prod(X1, X2) -> prod(X1, X2)
     , a__p(X) -> p(X)
     , a__add(X1, X2) -> add(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP*

Execution Time (secs)	0.133
Answer	MAYBE
Input	Transformed CSR 04 ExIntrod Zan97 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__fact(X) ->
       a__if(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__prod(0(), X) -> 0()
     , a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y)))
     , a__if(true(), X, Y) -> mark(X)
     , a__if(false(), X, Y) -> mark(Y)
     , a__zero(0()) -> true()
     , a__zero(s(X)) -> false()
     , a__p(s(X)) -> mark(X)
     , mark(fact(X)) -> a__fact(mark(X))
     , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
     , mark(zero(X)) -> a__zero(mark(X))
     , mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2))
     , mark(p(X)) -> a__p(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(true()) -> true()
     , mark(false()) -> false()
     , a__fact(X) -> fact(X)
     , a__if(X1, X2, X3) -> if(X1, X2, X3)
     , a__zero(X) -> zero(X)
     , a__prod(X1, X2) -> prod(X1, X2)
     , a__p(X) -> p(X)
     , a__add(X1, X2) -> add(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.158
Answer	MAYBE
Input	Transformed CSR 04 ExIntrod Zan97 GM

MAYBE

We consider the following Problem:

  Strict Trs:
    {  a__fact(X) ->
       a__if(a__zero(mark(X)), s(0()), prod(X, fact(p(X))))
     , a__add(0(), X) -> mark(X)
     , a__add(s(X), Y) -> s(a__add(mark(X), mark(Y)))
     , a__prod(0(), X) -> 0()
     , a__prod(s(X), Y) -> a__add(mark(Y), a__prod(mark(X), mark(Y)))
     , a__if(true(), X, Y) -> mark(X)
     , a__if(false(), X, Y) -> mark(Y)
     , a__zero(0()) -> true()
     , a__zero(s(X)) -> false()
     , a__p(s(X)) -> mark(X)
     , mark(fact(X)) -> a__fact(mark(X))
     , mark(if(X1, X2, X3)) -> a__if(mark(X1), X2, X3)
     , mark(zero(X)) -> a__zero(mark(X))
     , mark(prod(X1, X2)) -> a__prod(mark(X1), mark(X2))
     , mark(p(X)) -> a__p(mark(X))
     , mark(add(X1, X2)) -> a__add(mark(X1), mark(X2))
     , mark(s(X)) -> s(mark(X))
     , mark(0()) -> 0()
     , mark(true()) -> true()
     , mark(false()) -> false()
     , a__fact(X) -> fact(X)
     , a__if(X1, X2, X3) -> if(X1, X2, X3)
     , a__zero(X) -> zero(X)
     , a__prod(X1, X2) -> prod(X1, X2)
     , a__p(X) -> p(X)
     , a__add(X1, X2) -> add(X1, X2)}
  StartTerms: basic terms
  Strategy: innermost

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Problem Transformed CSR 04 ExIntrod Zan97 GM

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)