LMPO

Execution Time (secs)	0.038
Answer	YES(?,ELEMENTARY)
Input	SK90 2.59

YES(?,ELEMENTARY)

We consider the following Problem:

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

Hurray, we answered YES(?,ELEMENTARY)

MPO

Execution Time (secs)	0.029
Answer	YES(?,PRIMREC)
Input	SK90 2.59

YES(?,PRIMREC)

We consider the following Problem:

  Strict Trs: {f(g(x), y, y) -> g(f(x, x, y))}
  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)	0.035
Answer	YES(?,POLY)
Input	SK90 2.59

YES(?,POLY)

We consider the following Problem:

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

Hurray, we answered YES(?,POLY)

POP* (PS)

Execution Time (secs)	0.049
Answer	YES(?,POLY)
Input	SK90 2.59

YES(?,POLY)

We consider the following Problem:

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

Hurray, we answered YES(?,POLY)

Small POP*

Execution Time (secs)	0.055
Answer	MAYBE
Input	SK90 2.59

MAYBE

We consider the following Problem:

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

Certificate: MAYBE

Proof:
  The input cannot be shown compatible

Arrrr..

Small POP* (PS)

Execution Time (secs)	0.048
Answer	YES(?,O(n^1))
Input	SK90 2.59

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs: {f(g(x), y, y) -> g(f(x, x, y))}
  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) = {2, 3}, 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); y, y) -> g(; f(x; x, y))}
   Weak Trs  : {}

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

Problem SK90 2.59

LMPO

MPO

POP*

POP* (PS)

Small POP*

Small POP* (PS)