LMPO

Execution Time (secs)	0.068
Answer	YES(?,ELEMENTARY)
Input	Transformed CSR 04 ExConc Zan97 FR

YES(?,ELEMENTARY)

We consider the following Problem:

  Strict Trs:
    {  f(X) -> g(n__h(n__f(X)))
     , h(X) -> n__h(X)
     , f(X) -> n__f(X)
     , activate(n__h(X)) -> h(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , activate(X) -> 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) = {1}, safe(g) = {1}, safe(n__h) = {1}, safe(n__f) = {1},
   safe(h) = {1}, safe(activate) = {}

  and precedence

   activate > f, activate > h .

  Following symbols are considered recursive:

   {f, h, activate}

  The recursion depth is 2 .

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

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(; X) -> g(; n__h(; n__f(; X)))
      , h(; X) -> n__h(; X)
      , f(; X) -> n__f(; X)
      , activate(n__h(; X);) -> h(; activate(X;))
      , activate(n__f(; X);) -> f(; activate(X;))
      , activate(X;) -> X}
   Weak Trs  : {}

Hurray, we answered YES(?,ELEMENTARY)

MPO

Execution Time (secs)	0.066
Answer	YES(?,PRIMREC)
Input	Transformed CSR 04 ExConc Zan97 FR

YES(?,PRIMREC)

We consider the following Problem:

  Strict Trs:
    {  f(X) -> g(n__h(n__f(X)))
     , h(X) -> n__h(X)
     , f(X) -> n__f(X)
     , activate(n__h(X)) -> h(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , activate(X) -> 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, f > n__h, f > n__f, h > n__h, activate > f, activate > h .

Hurray, we answered YES(?,PRIMREC)

POP*

Execution Time (secs)	0.033
Answer	YES(?,POLY)
Input	Transformed CSR 04 ExConc Zan97 FR

YES(?,POLY)

We consider the following Problem:

  Strict Trs:
    {  f(X) -> g(n__h(n__f(X)))
     , h(X) -> n__h(X)
     , f(X) -> n__f(X)
     , activate(n__h(X)) -> h(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , activate(X) -> 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) = {1}, safe(g) = {1}, safe(n__h) = {1}, safe(n__f) = {1},
   safe(h) = {1}, safe(activate) = {}

  and precedence

   activate > f, activate > h .

  Following symbols are considered recursive:

   {f, h, activate}

  The recursion depth is 2 .

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

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(; X) -> g(; n__h(; n__f(; X)))
      , h(; X) -> n__h(; X)
      , f(; X) -> n__f(; X)
      , activate(n__h(; X);) -> h(; activate(X;))
      , activate(n__f(; X);) -> f(; activate(X;))
      , activate(X;) -> X}
   Weak Trs  : {}

Hurray, we answered YES(?,POLY)

POP* (PS)

Execution Time (secs)	0.041
Answer	YES(?,POLY)
Input	Transformed CSR 04 ExConc Zan97 FR

YES(?,POLY)

We consider the following Problem:

  Strict Trs:
    {  f(X) -> g(n__h(n__f(X)))
     , h(X) -> n__h(X)
     , f(X) -> n__f(X)
     , activate(n__h(X)) -> h(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , activate(X) -> 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) = {1}, safe(g) = {1}, safe(n__h) = {1}, safe(n__f) = {1},
   safe(h) = {1}, safe(activate) = {}

  and precedence

   activate > f, activate > h .

  Following symbols are considered recursive:

   {f, h, activate}

  The recursion depth is 2 .

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

   Strict DPs: {}
   Weak DPs  : {}
   Strict Trs:
     {  f(; X) -> g(; n__h(; n__f(; X)))
      , h(; X) -> n__h(; X)
      , f(; X) -> n__f(; X)
      , activate(n__h(; X);) -> h(; activate(X;))
      , activate(n__f(; X);) -> f(; activate(X;))
      , activate(X;) -> X}
   Weak Trs  : {}

Hurray, we answered YES(?,POLY)

Small POP*

Execution Time (secs)	0.111
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExConc Zan97 FR

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(X) -> g(n__h(n__f(X)))
     , h(X) -> n__h(X)
     , f(X) -> n__f(X)
     , activate(n__h(X)) -> h(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , activate(X) -> 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,
                             Nat 1-bounded) as induced by the safe mapping

   safe(f) = {1}, safe(g) = {1}, safe(n__h) = {1}, safe(n__f) = {1},
   safe(h) = {1}, safe(activate) = {}

  and precedence

   activate > f, activate > h .

  Following symbols are considered recursive:

   {activate}

  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(; X) -> g(; n__h(; n__f(; X)))
      , h(; X) -> n__h(; X)
      , f(; X) -> n__f(; X)
      , activate(n__h(; X);) -> h(; activate(X;))
      , activate(n__f(; X);) -> f(; activate(X;))
      , activate(X;) -> X}
   Weak Trs  : {}

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

Small POP* (PS)

Execution Time (secs)	0.072
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 ExConc Zan97 FR

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  f(X) -> g(n__h(n__f(X)))
     , h(X) -> n__h(X)
     , f(X) -> n__f(X)
     , activate(n__h(X)) -> h(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , activate(X) -> 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,
                             Nat 1-bounded) as induced by the safe mapping

   safe(f) = {1}, safe(g) = {1}, safe(n__h) = {1}, safe(n__f) = {1},
   safe(h) = {1}, safe(activate) = {}

  and precedence

   activate > f, activate > h .

  Following symbols are considered recursive:

   {activate}

  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(; X) -> g(; n__h(; n__f(; X)))
      , h(; X) -> n__h(; X)
      , f(; X) -> n__f(; X)
      , activate(n__h(; X);) -> h(; activate(X;))
      , activate(n__f(; X);) -> f(; activate(X;))
      , activate(X;) -> X}
   Weak Trs  : {}

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

Problem Transformed CSR 04 ExConc Zan97 FR

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)