Problem Mixed TRS jones4

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed TRS jones4

stdout:

YES(?,O(n^1))

Problem:
p(m,n,s(r)) -> p(m,r,n)
p(m,s(n),0()) -> p(0(),n,m)
p(m,0(),0()) -> m

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    p1(1,1,1) -> 3*
    p1(2,2,1) -> 3*
    p1(1,1,2) -> 3*
    p1(2,2,2) -> 3*
    p1(1,2,1) -> 3*
    p1(2,1,1) -> 3*
    p1(1,2,2) -> 3*
    p1(2,1,2) -> 3*
    01() -> 1*
    p0(1,1,1) -> 3*
    p0(2,2,1) -> 3*
    p0(1,1,2) -> 3*
    p0(2,2,2) -> 3*
    p0(1,2,1) -> 3*
    p0(2,1,1) -> 3*
    p0(1,2,2) -> 3*
    p0(2,1,2) -> 3*
    s0(2) -> 1*
    s0(1) -> 1*
    00() -> 2*
    1 -> 3*
    2 -> 3*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed TRS jones4

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed TRS jones4

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:
    {  p(m, n, s(r)) -> p(m, r, n)
     , p(m, s(n), 0()) -> p(0(), n, m)
     , p(m, 0(), 0()) -> m}

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:
         {  p(m, n, s(r)) -> p(m, r, n)
          , p(m, s(n), 0()) -> p(0(), n, m)
          , p(m, 0(), 0()) -> m}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  p_0(2, 2, 2) -> 1
        , p_1(2, 2, 2) -> 1
        , s_0(2) -> 1
        , s_0(2) -> 2
        , 0_0() -> 1
        , 0_0() -> 2
        , 0_1() -> 1
        , 0_1() -> 2}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed TRS jones4

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed TRS jones4

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  p(m, n, s(r)) -> p(m, r, n)
     , p(m, s(n), 0()) -> p(0(), n, m)
     , p(m, 0(), 0()) -> m}

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:
         {  p(m, n, s(r)) -> p(m, r, n)
          , p(m, s(n), 0()) -> p(0(), n, m)
          , p(m, 0(), 0()) -> m}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  p_0(2, 2, 2) -> 1
        , p_1(2, 2, 2) -> 1
        , s_0(2) -> 1
        , s_0(2) -> 2
        , 0_0() -> 1
        , 0_0() -> 2
        , 0_1() -> 1
        , 0_1() -> 2}