LMPO

Execution Time (secs)	0.033
Answer	YES(?,ELEMENTARY)
Input	Der95 06

YES(?,ELEMENTARY)

We consider the following Problem:

  Strict Trs:
    {  f(g(x)) -> g(g(f(x)))
     , f(g(x)) -> g(g(g(x)))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,ELEMENTARY)

Proof:
  The input was oriented with the instance of
  Lightweight Multiset Path Order () as induced by the safe mapping

   safe(f) = {}, safe(g) = {1}

  and precedence

   empty .

  Following symbols are considered recursive:

   {f}

  The recursion depth is 1 .

  For your convenience, here are the oriented rules in predicative
  notation (possibly applying argument filtering):

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(g(; x);) -> g(; g(; f(x;)))
      , f(g(; x);) -> g(; g(; g(; x)))}
   Weak Trs  : {}

Hurray, we answered YES(?,ELEMENTARY)

MPO

Execution Time (secs)	0.034
Answer	YES(?,PRIMREC)
Input	Der95 06

YES(?,PRIMREC)

We consider the following Problem:

  Strict Trs:
    {  f(g(x)) -> g(g(f(x)))
     , f(g(x)) -> g(g(g(x)))}
  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

   f > g .

Hurray, we answered YES(?,PRIMREC)

POP*

Execution Time (secs)	0.051
Answer	YES(?,POLY)
Input	Der95 06

YES(?,POLY)

We consider the following Problem:

  Strict Trs:
    {  f(g(x)) -> g(g(f(x)))
     , f(g(x)) -> g(g(g(x)))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,POLY)

Proof:
  The input was oriented with the instance of
  Polynomial Path Order () as induced by the safe mapping

   safe(f) = {}, safe(g) = {1}

  and precedence

   empty .

  Following symbols are considered recursive:

   {f}

  The recursion depth is 1 .

  For your convenience, here are the oriented rules in predicative
  notation (possibly applying argument filtering):

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(g(; x);) -> g(; g(; f(x;)))
      , f(g(; x);) -> g(; g(; g(; x)))}
   Weak Trs  : {}

Hurray, we answered YES(?,POLY)

POP* (PS)

Execution Time (secs)	0.024
Answer	YES(?,POLY)
Input	Der95 06

YES(?,POLY)

We consider the following Problem:

  Strict Trs:
    {  f(g(x)) -> g(g(f(x)))
     , f(g(x)) -> g(g(g(x)))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,POLY)

Proof:
  The input was oriented with the instance of
  Polynomial Path Order (PS) as induced by the safe mapping

   safe(f) = {}, safe(g) = {1}

  and precedence

   empty .

  Following symbols are considered recursive:

   {f}

  The recursion depth is 1 .

  For your convenience, here are the oriented rules in predicative
  notation (possibly applying argument filtering):

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(g(; x);) -> g(; g(; f(x;)))
      , f(g(; x);) -> g(; g(; g(; x)))}
   Weak Trs  : {}

Hurray, we answered YES(?,POLY)

Small POP*

Execution Time (secs)	0.053
Answer	YES(?,O(n^1))
Input	Der95 06

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(g(x)) -> g(g(f(x)))
     , f(g(x)) -> g(g(g(x)))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^1))

Proof:
  The input was oriented with the instance of
  Small Polynomial Path Order (WSC) as induced by the safe mapping

   safe(f) = {}, safe(g) = {1}

  and precedence

   empty .

  Following symbols are considered recursive:

   {f}

  The recursion depth is 1 .

  For your convenience, here are the oriented rules in predicative
  notation (possibly applying argument filtering):

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(g(; x);) -> g(; g(; f(x;)))
      , f(g(; x);) -> g(; g(; g(; x)))}
   Weak Trs  : {}

Hurray, we answered YES(?,O(n^1))

Small POP* (PS)

Execution Time (secs)	0.033
Answer	YES(?,O(n^1))
Input	Der95 06

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(g(x)) -> g(g(f(x)))
     , f(g(x)) -> g(g(g(x)))}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^1))

Proof:
  The input was oriented with the instance of
  Small Polynomial Path Order (WSC,
                             PS) as induced by the safe mapping

   safe(f) = {}, safe(g) = {1}

  and precedence

   empty .

  Following symbols are considered recursive:

   {f}

  The recursion depth is 1 .

  For your convenience, here are the oriented rules in predicative
  notation (possibly applying argument filtering):

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(g(; x);) -> g(; g(; f(x;)))
      , f(g(; x);) -> g(; g(; g(; x)))}
   Weak Trs  : {}

Hurray, we answered YES(?,O(n^1))

Problem Der95 06

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)