Problem Mixed SRS turing add

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed SRS turing add

stdout:

YES(?,O(n^1))

Problem:
1(q0(1(x1))) -> 0(1(q1(x1)))
1(q0(0(x1))) -> 0(0(q1(x1)))
1(q1(1(x1))) -> 1(1(q1(x1)))
1(q1(0(x1))) -> 1(0(q1(x1)))
0(q1(x1)) -> q2(1(x1))
1(q2(x1)) -> q2(1(x1))
0(q2(x1)) -> 0(q0(x1))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4}
   transitions:
    01(21) -> 22*
    q01(30) -> 31*
    q01(20) -> 21*
    q01(28) -> 29*
    q21(7) -> 8*
    11(14) -> 15*
    11(16) -> 17*
    11(6) -> 7*
    10(2) -> 4*
    10(1) -> 4*
    10(3) -> 4*
    q00(2) -> 1*
    q00(1) -> 1*
    q00(3) -> 1*
    00(2) -> 5*
    00(1) -> 5*
    00(3) -> 5*
    q10(2) -> 2*
    q10(1) -> 2*
    q10(3) -> 2*
    q20(2) -> 3*
    q20(1) -> 3*
    q20(3) -> 3*
    1 -> 28,14
    2 -> 20,6
    3 -> 30,16
    8 -> 17,7,4,5
    15 -> 7*
    17 -> 7*
    22 -> 5*
    29 -> 21*
    31 -> 21*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed SRS turing add

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed SRS turing add

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:
    {  1(q0(1(x1))) -> 0(1(q1(x1)))
     , 1(q0(0(x1))) -> 0(0(q1(x1)))
     , 1(q1(1(x1))) -> 1(1(q1(x1)))
     , 1(q1(0(x1))) -> 1(0(q1(x1)))
     , 0(q1(x1)) -> q2(1(x1))
     , 1(q2(x1)) -> q2(1(x1))
     , 0(q2(x1)) -> 0(q0(x1))}

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:
         {  1(q0(1(x1))) -> 0(1(q1(x1)))
          , 1(q0(0(x1))) -> 0(0(q1(x1)))
          , 1(q1(1(x1))) -> 1(1(q1(x1)))
          , 1(q1(0(x1))) -> 1(0(q1(x1)))
          , 0(q1(x1)) -> q2(1(x1))
          , 1(q2(x1)) -> q2(1(x1))
          , 0(q2(x1)) -> 0(q0(x1))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  1_0(2) -> 1
        , 1_1(2) -> 3
        , q0_0(2) -> 2
        , q0_1(2) -> 4
        , 0_0(2) -> 1
        , 0_1(4) -> 1
        , q1_0(2) -> 2
        , q2_0(2) -> 2
        , q2_1(3) -> 1
        , q2_1(3) -> 3}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed SRS turing add

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed SRS turing add

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  1(q0(1(x1))) -> 0(1(q1(x1)))
     , 1(q0(0(x1))) -> 0(0(q1(x1)))
     , 1(q1(1(x1))) -> 1(1(q1(x1)))
     , 1(q1(0(x1))) -> 1(0(q1(x1)))
     , 0(q1(x1)) -> q2(1(x1))
     , 1(q2(x1)) -> q2(1(x1))
     , 0(q2(x1)) -> 0(q0(x1))}

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:
         {  1(q0(1(x1))) -> 0(1(q1(x1)))
          , 1(q0(0(x1))) -> 0(0(q1(x1)))
          , 1(q1(1(x1))) -> 1(1(q1(x1)))
          , 1(q1(0(x1))) -> 1(0(q1(x1)))
          , 0(q1(x1)) -> q2(1(x1))
          , 1(q2(x1)) -> q2(1(x1))
          , 0(q2(x1)) -> 0(q0(x1))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  1_0(2) -> 1
        , 1_1(2) -> 3
        , q0_0(2) -> 2
        , q0_1(2) -> 4
        , 0_0(2) -> 1
        , 0_1(4) -> 1
        , q1_0(2) -> 2
        , q2_0(2) -> 2
        , q2_1(3) -> 1
        , q2_1(3) -> 3}