Problem Maude 06 PALINDROME nokinds-noand

Tool IRC1

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

stdout:

YES(?,O(n^1))

Tool IRC2

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

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
     , U11(tt()) -> tt()
     , U21(tt(), V2) -> U22(isList(V2))
     , U22(tt()) -> tt()
     , U31(tt()) -> tt()
     , U41(tt(), V2) -> U42(isNeList(V2))
     , U42(tt()) -> tt()
     , U51(tt(), V2) -> U52(isList(V2))
     , U52(tt()) -> tt()
     , U61(tt()) -> tt()
     , U71(tt(), P) -> U72(isPal(P))
     , U72(tt()) -> tt()
     , U81(tt()) -> tt()
     , isList(V) -> U11(isNeList(V))
     , isList(nil()) -> tt()
     , isList(__(V1, V2)) -> U21(isList(V1), V2)
     , isNeList(V) -> U31(isQid(V))
     , isNeList(__(V1, V2)) -> U41(isList(V1), V2)
     , isNeList(__(V1, V2)) -> U51(isNeList(V1), V2)
     , isNePal(V) -> U61(isQid(V))
     , isNePal(__(I, __(P, I))) -> U71(isQid(I), P)
     , isPal(V) -> U81(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
          , U11(tt()) -> tt()
          , U21(tt(), V2) -> U22(isList(V2))
          , U22(tt()) -> tt()
          , U31(tt()) -> tt()
          , U41(tt(), V2) -> U42(isNeList(V2))
          , U42(tt()) -> tt()
          , U51(tt(), V2) -> U52(isList(V2))
          , U52(tt()) -> tt()
          , U61(tt()) -> tt()
          , U71(tt(), P) -> U72(isPal(P))
          , U72(tt()) -> tt()
          , U81(tt()) -> tt()
          , isList(V) -> U11(isNeList(V))
          , isList(nil()) -> tt()
          , isList(__(V1, V2)) -> U21(isList(V1), V2)
          , isNeList(V) -> U31(isQid(V))
          , isNeList(__(V1, V2)) -> U41(isList(V1), V2)
          , isNeList(__(V1, V2)) -> U51(isNeList(V1), V2)
          , isNePal(V) -> U61(isQid(V))
          , isNePal(__(I, __(P, I))) -> U71(isQid(I), P)
          , isPal(V) -> U81(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 3.
       The enriched problem is compatible with the following automaton:
       {  ___0(2, 2) -> 1
        , nil_0() -> 1
        , nil_0() -> 2
        , U11_0(2) -> 1
        , U11_1(4) -> 1
        , U11_2(6) -> 3
        , tt_0() -> 1
        , tt_0() -> 2
        , tt_1() -> 1
        , tt_1() -> 3
        , tt_1() -> 5
        , tt_1() -> 7
        , tt_1() -> 8
        , tt_1() -> 9
        , tt_2() -> 1
        , tt_2() -> 4
        , tt_2() -> 6
        , tt_2() -> 10
        , tt_2() -> 11
        , tt_3() -> 3
        , tt_3() -> 5
        , U21_0(2, 2) -> 1
        , U22_0(2) -> 1
        , U22_1(3) -> 1
        , isList_0(2) -> 1
        , isList_1(2) -> 3
        , U31_0(2) -> 1
        , U31_1(7) -> 1
        , U31_2(8) -> 4
        , U31_3(9) -> 6
        , U41_0(2, 2) -> 1
        , U42_0(2) -> 1
        , U42_1(4) -> 1
        , isNeList_0(2) -> 1
        , isNeList_1(2) -> 4
        , isNeList_2(2) -> 6
        , U51_0(2, 2) -> 1
        , U52_0(2) -> 1
        , U52_1(3) -> 1
        , U61_0(2) -> 1
        , U61_1(7) -> 1
        , U61_2(8) -> 10
        , U61_3(9) -> 11
        , U71_0(2, 2) -> 1
        , U72_0(2) -> 1
        , U72_1(5) -> 1
        , isPal_0(2) -> 1
        , isPal_1(2) -> 5
        , U81_0(2) -> 1
        , U81_1(10) -> 1
        , U81_2(11) -> 5
        , isQid_0(2) -> 1
        , isQid_1(2) -> 7
        , isQid_2(2) -> 8
        , isQid_3(2) -> 9
        , isNePal_0(2) -> 1
        , isNePal_1(2) -> 10
        , isNePal_2(2) -> 11
        , 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}

Tool RC1

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

stdout:

YES(?,O(n^1))

Tool RC2

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

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
     , U11(tt()) -> tt()
     , U21(tt(), V2) -> U22(isList(V2))
     , U22(tt()) -> tt()
     , U31(tt()) -> tt()
     , U41(tt(), V2) -> U42(isNeList(V2))
     , U42(tt()) -> tt()
     , U51(tt(), V2) -> U52(isList(V2))
     , U52(tt()) -> tt()
     , U61(tt()) -> tt()
     , U71(tt(), P) -> U72(isPal(P))
     , U72(tt()) -> tt()
     , U81(tt()) -> tt()
     , isList(V) -> U11(isNeList(V))
     , isList(nil()) -> tt()
     , isList(__(V1, V2)) -> U21(isList(V1), V2)
     , isNeList(V) -> U31(isQid(V))
     , isNeList(__(V1, V2)) -> U41(isList(V1), V2)
     , isNeList(__(V1, V2)) -> U51(isNeList(V1), V2)
     , isNePal(V) -> U61(isQid(V))
     , isNePal(__(I, __(P, I))) -> U71(isQid(I), P)
     , isPal(V) -> U81(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
          , U11(tt()) -> tt()
          , U21(tt(), V2) -> U22(isList(V2))
          , U22(tt()) -> tt()
          , U31(tt()) -> tt()
          , U41(tt(), V2) -> U42(isNeList(V2))
          , U42(tt()) -> tt()
          , U51(tt(), V2) -> U52(isList(V2))
          , U52(tt()) -> tt()
          , U61(tt()) -> tt()
          , U71(tt(), P) -> U72(isPal(P))
          , U72(tt()) -> tt()
          , U81(tt()) -> tt()
          , isList(V) -> U11(isNeList(V))
          , isList(nil()) -> tt()
          , isList(__(V1, V2)) -> U21(isList(V1), V2)
          , isNeList(V) -> U31(isQid(V))
          , isNeList(__(V1, V2)) -> U41(isList(V1), V2)
          , isNeList(__(V1, V2)) -> U51(isNeList(V1), V2)
          , isNePal(V) -> U61(isQid(V))
          , isNePal(__(I, __(P, I))) -> U71(isQid(I), P)
          , isPal(V) -> U81(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 3.
       The enriched problem is compatible with the following automaton:
       {  ___0(2, 2) -> 1
        , nil_0() -> 1
        , nil_0() -> 2
        , U11_0(2) -> 1
        , U11_1(4) -> 1
        , U11_2(6) -> 3
        , tt_0() -> 1
        , tt_0() -> 2
        , tt_1() -> 1
        , tt_1() -> 3
        , tt_1() -> 5
        , tt_1() -> 7
        , tt_1() -> 8
        , tt_1() -> 9
        , tt_2() -> 1
        , tt_2() -> 4
        , tt_2() -> 6
        , tt_2() -> 10
        , tt_2() -> 11
        , tt_3() -> 3
        , tt_3() -> 5
        , U21_0(2, 2) -> 1
        , U22_0(2) -> 1
        , U22_1(3) -> 1
        , isList_0(2) -> 1
        , isList_1(2) -> 3
        , U31_0(2) -> 1
        , U31_1(7) -> 1
        , U31_2(8) -> 4
        , U31_3(9) -> 6
        , U41_0(2, 2) -> 1
        , U42_0(2) -> 1
        , U42_1(4) -> 1
        , isNeList_0(2) -> 1
        , isNeList_1(2) -> 4
        , isNeList_2(2) -> 6
        , U51_0(2, 2) -> 1
        , U52_0(2) -> 1
        , U52_1(3) -> 1
        , U61_0(2) -> 1
        , U61_1(7) -> 1
        , U61_2(8) -> 10
        , U61_3(9) -> 11
        , U71_0(2, 2) -> 1
        , U72_0(2) -> 1
        , U72_1(5) -> 1
        , isPal_0(2) -> 1
        , isPal_1(2) -> 5
        , U81_0(2) -> 1
        , U81_1(10) -> 1
        , U81_2(11) -> 5
        , isQid_0(2) -> 1
        , isQid_1(2) -> 7
        , isQid_2(2) -> 8
        , isQid_3(2) -> 9
        , isNePal_0(2) -> 1
        , isNePal_1(2) -> 10
        , isNePal_2(2) -> 11
        , 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}