LMPO

Execution Time (secs)	0.030
Answer	YES(?,ELEMENTARY)
Input	AG01 3.35

YES(?,ELEMENTARY)

We consider the following Problem:

  Strict Trs:
    {  g(s(x)) -> f(x)
     , f(0()) -> s(0())
     , f(s(x)) -> s(s(g(x)))
     , g(0()) -> 0()}
  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(g) = {}, safe(s) = {1}, safe(f) = {}, safe(0) = {}

  and precedence

   g ~ f .

  Following symbols are considered recursive:

   {g, 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:
     {  g(s(; x);) -> f(x;)
      , f(0();) -> s(; 0())
      , f(s(; x);) -> s(; s(; g(x;)))
      , g(0();) -> 0()}
   Weak Trs  : {}

Hurray, we answered YES(?,ELEMENTARY)

MPO

Execution Time (secs)	0.033
Answer	YES(?,PRIMREC)
Input	AG01 3.35

YES(?,PRIMREC)

We consider the following Problem:

  Strict Trs:
    {  g(s(x)) -> f(x)
     , f(0()) -> s(0())
     , f(s(x)) -> s(s(g(x)))
     , g(0()) -> 0()}
  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 > s, g ~ f .

Hurray, we answered YES(?,PRIMREC)

POP*

Execution Time (secs)	0.039
Answer	YES(?,POLY)
Input	AG01 3.35

YES(?,POLY)

We consider the following Problem:

  Strict Trs:
    {  g(s(x)) -> f(x)
     , f(0()) -> s(0())
     , f(s(x)) -> s(s(g(x)))
     , g(0()) -> 0()}
  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(g) = {}, safe(s) = {1}, safe(f) = {}, safe(0) = {}

  and precedence

   g ~ f .

  Following symbols are considered recursive:

   {g, 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:
     {  g(s(; x);) -> f(x;)
      , f(0();) -> s(; 0())
      , f(s(; x);) -> s(; s(; g(x;)))
      , g(0();) -> 0()}
   Weak Trs  : {}

Hurray, we answered YES(?,POLY)

POP* (PS)

Execution Time (secs)	0.032
Answer	YES(?,POLY)
Input	AG01 3.35

YES(?,POLY)

We consider the following Problem:

  Strict Trs:
    {  g(s(x)) -> f(x)
     , f(0()) -> s(0())
     , f(s(x)) -> s(s(g(x)))
     , g(0()) -> 0()}
  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(g) = {}, safe(s) = {1}, safe(f) = {}, safe(0) = {}

  and precedence

   g ~ f .

  Following symbols are considered recursive:

   {g, 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:
     {  g(s(; x);) -> f(x;)
      , f(0();) -> s(; 0())
      , f(s(; x);) -> s(; s(; g(x;)))
      , g(0();) -> 0()}
   Weak Trs  : {}

Hurray, we answered YES(?,POLY)

Small POP*

Execution Time (secs)	0.042
Answer	YES(?,O(n^1))
Input	AG01 3.35

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  g(s(x)) -> f(x)
     , f(0()) -> s(0())
     , f(s(x)) -> s(s(g(x)))
     , g(0()) -> 0()}
  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(g) = {}, safe(s) = {1}, safe(f) = {}, safe(0) = {}

  and precedence

   g ~ f .

  Following symbols are considered recursive:

   {g, 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:
     {  g(s(; x);) -> f(x;)
      , f(0();) -> s(; 0())
      , f(s(; x);) -> s(; s(; g(x;)))
      , g(0();) -> 0()}
   Weak Trs  : {}

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

Small POP* (PS)

Execution Time (secs)	0.037
Answer	YES(?,O(n^1))
Input	AG01 3.35

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  g(s(x)) -> f(x)
     , f(0()) -> s(0())
     , f(s(x)) -> s(s(g(x)))
     , g(0()) -> 0()}
  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(g) = {}, safe(s) = {1}, safe(f) = {}, safe(0) = {}

  and precedence

   g ~ f .

  Following symbols are considered recursive:

   {g, 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:
     {  g(s(; x);) -> f(x;)
      , f(0();) -> s(; 0())
      , f(s(; x);) -> s(; s(; g(x;)))
      , g(0();) -> 0()}
   Weak Trs  : {}

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

Problem AG01 3.35

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)