Problem Maude 06 PALINDROME nokinds

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Maude 06 PALINDROME nokinds

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Maude 06 PALINDROME nokinds

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  __(__(X, Y), Z) -> __(X, __(Y, Z))
     , __(X, nil()) -> X
     , __(nil(), X) -> X
     , and(tt(), X) -> X
     , isList(V) -> isNeList(V)
     , isList(nil()) -> tt()
     , isList(__(V1, V2)) -> and(isList(V1), isList(V2))
     , isNeList(V) -> isQid(V)
     , isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
     , isNeList(__(V1, V2)) -> and(isNeList(V1), isList(V2))
     , isNePal(V) -> isQid(V)
     , isNePal(__(I, __(P, I))) -> and(isQid(I), isPal(P))
     , isPal(V) -> isNePal(V)
     , isPal(nil()) -> tt()
     , isQid(a()) -> tt()
     , isQid(e()) -> tt()
     , isQid(i()) -> tt()
     , isQid(o()) -> tt()
     , isQid(u()) -> tt()}

Proof Output:
  'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:

  Details:
  --------
    'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with minimal-enrichment and initial automaton 'match''
     --------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    innermost runtime-complexity with respect to
       Rules:
         {  __(__(X, Y), Z) -> __(X, __(Y, Z))
          , __(X, nil()) -> X
          , __(nil(), X) -> X
          , and(tt(), X) -> X
          , isList(V) -> isNeList(V)
          , isList(nil()) -> tt()
          , isList(__(V1, V2)) -> and(isList(V1), isList(V2))
          , isNeList(V) -> isQid(V)
          , isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
          , isNeList(__(V1, V2)) -> and(isNeList(V1), isList(V2))
          , isNePal(V) -> isQid(V)
          , isNePal(__(I, __(P, I))) -> and(isQid(I), isPal(P))
          , isPal(V) -> isNePal(V)
          , isPal(nil()) -> tt()
          , isQid(a()) -> tt()
          , isQid(e()) -> tt()
          , isQid(i()) -> tt()

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Maude 06 PALINDROME nokinds

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Maude 06 PALINDROME nokinds

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  __(__(X, Y), Z) -> __(X, __(Y, Z))
     , __(X, nil()) -> X
     , __(nil(), X) -> X
     , and(tt(), X) -> X
     , isList(V) -> isNeList(V)
     , isList(nil()) -> tt()
     , isList(__(V1, V2)) -> and(isList(V1), isList(V2))
     , isNeList(V) -> isQid(V)
     , isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
     , isNeList(__(V1, V2)) -> and(isNeList(V1), isList(V2))
     , isNePal(V) -> isQid(V)
     , isNePal(__(I, __(P, I))) -> and(isQid(I), isPal(P))
     , isPal(V) -> isNePal(V)
     , isPal(nil()) -> tt()
     , isQid(a()) -> tt()
     , isQid(e()) -> tt()
     , isQid(i()) -> tt()
     , isQid(o()) -> tt()
     , isQid(u()) -> tt()}

Proof Output:
  'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:

  Details:
  --------
    'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
     'Bounds with minimal-enrichment and initial automaton 'match''
     --------------------------------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    runtime-complexity with respect to
       Rules:
         {  __(__(X, Y), Z) -> __(X, __(Y, Z))
          , __(X, nil()) -> X
          , __(nil(), X) -> X
          , and(tt(), X) -> X
          , isList(V) -> isNeList(V)
          , isList(nil()) -> tt()
          , isList(__(V1, V2)) -> and(isList(V1), isList(V2))
          , isNeList(V) -> isQid(V)
          , isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
          , isNeList(__(V1, V2)) -> and(isNeList(V1), isList(V2))
          , isNePal(V) -> isQid(V)
          , isNePal(__(I, __(P, I))) -> and(isQid(I), isPal(P))
          , isPal(V) -> isNePal(V)
          , isPal(nil()) -> tt()
          , isQid(a()) -> tt()
          , isQid(e()) -> tt()
          , isQid(i()) -> tt()
          , isQid(o()) -> tt()
          , isQid(u()) -> tt()}

     Proof Output:
       The problem is match-bounded by 2.
       The enriched problem is compatible with the following automaton:
       {  ___0(2, 2) -> 1
        , nil_0() -> 1
        , nil_0() -> 2
        , and_0(2, 2) -> 1
        , tt_0() -> 1
        , tt_0() -> 2
        , tt_1() -> 1
        , isList_0(2) -> 1
        , isNeList_0(2) -> 1
        , isNeList_1(2) -> 1
        , isQid_0(2) -> 1
        , isQid_1(2) -> 1
        , isQid_2(2) -> 1
        , isNePal_0(2) -> 1
        , isNePal_1(2) -> 1
        , isPal_0(2) -> 1
        , a_0() -> 1
        , a_0() -> 2
        , e_0() -> 1
        , e_0() -> 2
        , i_0() -> 1
        , i_0() -> 2
        , o_0() -> 1
        , o_0() -> 2
        , u_0() -> 1
        , u_0() -> 2}