Problem Maude 06 MYNAT nosorts-noand-peanoSimple

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

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:
    {  U11(tt(), M, N) -> U12(tt(), M, N)
     , U12(tt(), M, N) -> s(plus(N, M))
     , plus(N, 0()) -> N
     , plus(N, s(M)) -> U11(tt(), M, N)}

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:
         {  U11(tt(), M, N) -> U12(tt(), M, N)
          , U12(tt(), M, N) -> s(plus(N, M))
          , plus(N, 0()) -> N
          , plus(N, s(M)) -> U11(tt(), M, N)}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  U11_0(2, 2, 2) -> 1
        , U11_1(3, 2, 2) -> 1
        , U11_1(3, 2, 2) -> 4
        , U11_1(3, 2, 2) -> 5
        , U11_1(3, 2, 2) -> 7
        , tt_0() -> 1
        , tt_0() -> 2
        , tt_0() -> 4
        , tt_0() -> 5
        , tt_0() -> 7
        , tt_1() -> 3
        , tt_2() -> 6
        , U12_0(2, 2, 2) -> 1
        , U12_1(3, 2, 2) -> 1
        , U12_2(6, 2, 2) -> 1
        , U12_2(6, 2, 2) -> 4
        , U12_2(6, 2, 2) -> 5
        , U12_2(6, 2, 2) -> 7
        , s_0(2) -> 1
        , s_0(2) -> 2
        , s_0(2) -> 4
        , s_0(2) -> 5
        , s_0(2) -> 7
        , s_1(4) -> 1
        , s_2(5) -> 1
        , s_3(7) -> 1
        , s_3(7) -> 4
        , s_3(7) -> 5
        , s_3(7) -> 7
        , plus_0(2, 2) -> 1
        , plus_1(2, 2) -> 4
        , plus_2(2, 2) -> 5
        , plus_3(2, 2) -> 7
        , 0_0() -> 1
        , 0_0() -> 2
        , 0_0() -> 4
        , 0_0() -> 5
        , 0_0() -> 7}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Maude 06 MYNAT nosorts-noand-peanoSimple

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  U11(tt(), M, N) -> U12(tt(), M, N)
     , U12(tt(), M, N) -> s(plus(N, M))
     , plus(N, 0()) -> N
     , plus(N, s(M)) -> U11(tt(), M, N)}

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:
         {  U11(tt(), M, N) -> U12(tt(), M, N)
          , U12(tt(), M, N) -> s(plus(N, M))
          , plus(N, 0()) -> N
          , plus(N, s(M)) -> U11(tt(), M, N)}

     Proof Output:
       The problem is match-bounded by 3.
       The enriched problem is compatible with the following automaton:
       {  U11_0(2, 2, 2) -> 1
        , U11_1(3, 2, 2) -> 1
        , U11_1(3, 2, 2) -> 4
        , U11_1(3, 2, 2) -> 5
        , U11_1(3, 2, 2) -> 7
        , tt_0() -> 1
        , tt_0() -> 2
        , tt_0() -> 4
        , tt_0() -> 5
        , tt_0() -> 7
        , tt_1() -> 3
        , tt_2() -> 6
        , U12_0(2, 2, 2) -> 1
        , U12_1(3, 2, 2) -> 1
        , U12_2(6, 2, 2) -> 1
        , U12_2(6, 2, 2) -> 4
        , U12_2(6, 2, 2) -> 5
        , U12_2(6, 2, 2) -> 7
        , s_0(2) -> 1
        , s_0(2) -> 2
        , s_0(2) -> 4
        , s_0(2) -> 5
        , s_0(2) -> 7
        , s_1(4) -> 1
        , s_2(5) -> 1
        , s_3(7) -> 1
        , s_3(7) -> 4
        , s_3(7) -> 5
        , s_3(7) -> 7
        , plus_0(2, 2) -> 1
        , plus_1(2, 2) -> 4
        , plus_2(2, 2) -> 5
        , plus_3(2, 2) -> 7
        , 0_0() -> 1
        , 0_0() -> 2
        , 0_0() -> 4
        , 0_0() -> 5
        , 0_0() -> 7}