Problem Various 04 18

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Various 04 18

stdout:

YES(?,O(n^1))

Problem:
+(*(x,y),*(x,z)) -> *(x,+(y,z))
+(+(x,y),z) -> +(x,+(y,z))
+(*(x,y),+(*(x,z),u())) -> +(*(x,+(y,z)),u())

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    +0(1,2) -> 3*
    +0(2,1) -> 3*
    +0(1,1) -> 3*
    +0(2,2) -> 3*
    *0(1,2) -> 1*
    *0(2,1) -> 1*
    *0(1,1) -> 1*
    *0(2,2) -> 1*
    u0() -> 2*
    *1(2,3) -> 3*
    *1(1,3) -> 3*
    +1(1,2) -> 3*
    +1(2,1) -> 3*
    +1(1,1) -> 3*
    +1(2,2) -> 3*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Various 04 18

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Various 04 18

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), *(x, z)) -> *(x, +(y, z))
     , +(+(x, y), z) -> +(x, +(y, z))
     , +(*(x, y), +(*(x, z), u())) -> +(*(x, +(y, z)), u())}

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), *(x, z)) -> *(x, +(y, z))
          , +(+(x, y), z) -> +(x, +(y, z))
          , +(*(x, y), +(*(x, z), u())) -> +(*(x, +(y, z)), u())}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  +_0(2, 2) -> 1
        , +_1(2, 2) -> 3
        , *_0(2, 2) -> 2
        , *_1(2, 3) -> 1
        , *_1(2, 3) -> 3
        , u_0() -> 2}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Various 04 18

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Various 04 18

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), *(x, z)) -> *(x, +(y, z))
     , +(+(x, y), z) -> +(x, +(y, z))
     , +(*(x, y), +(*(x, z), u())) -> +(*(x, +(y, z)), u())}

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), *(x, z)) -> *(x, +(y, z))
          , +(+(x, y), z) -> +(x, +(y, z))
          , +(*(x, y), +(*(x, z), u())) -> +(*(x, +(y, z)), u())}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  +_0(2, 2) -> 1
        , +_1(2, 2) -> 3
        , *_0(2, 2) -> 2
        , *_1(2, 3) -> 1
        , *_1(2, 3) -> 3
        , u_0() -> 2}