Problem Mixed innermost test830

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed innermost test830

stdout:

YES(?,O(n^1))

Problem:
f(s(X)) -> f(X)
g(cons(0(),Y)) -> g(Y)
g(cons(s(X),Y)) -> s(X)
h(cons(X,Y)) -> h(g(cons(X,Y)))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {6,5,4}
   transitions:
    h1(8) -> 6*
    g1(7) -> 8*
    g1(2) -> 8,5
    g1(1) -> 8,5
    g1(3) -> 8,5
    cons1(3,1) -> 7*
    cons1(3,3) -> 7*
    cons1(1,2) -> 7*
    cons1(2,1) -> 7*
    cons1(2,3) -> 7*
    cons1(3,2) -> 7*
    cons1(1,1) -> 7*
    cons1(1,3) -> 7*
    cons1(2,2) -> 7*
    s1(2) -> 8,5
    s1(1) -> 8,5
    s1(3) -> 8,5
    f1(2) -> 4*
    f1(1) -> 4*
    f1(3) -> 4*
    f0(2) -> 4*
    f0(1) -> 4*
    f0(3) -> 4*
    s0(2) -> 1*
    s0(1) -> 1*
    s0(3) -> 1*
    g0(2) -> 5*
    g0(1) -> 5*
    g0(3) -> 5*
    cons0(3,1) -> 2*
    cons0(3,3) -> 2*
    cons0(1,2) -> 2*
    cons0(2,1) -> 2*
    cons0(2,3) -> 2*
    cons0(3,2) -> 2*
    cons0(1,1) -> 2*
    cons0(1,3) -> 2*
    cons0(2,2) -> 2*
    00() -> 3*
    h0(2) -> 6*
    h0(1) -> 6*
    h0(3) -> 6*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed innermost test830

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed innermost test830

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:
    {  f(s(X)) -> f(X)
     , g(cons(0(), Y)) -> g(Y)
     , g(cons(s(X), Y)) -> s(X)
     , h(cons(X, Y)) -> h(g(cons(X, Y)))}

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:
         {  f(s(X)) -> f(X)
          , g(cons(0(), Y)) -> g(Y)
          , g(cons(s(X), Y)) -> s(X)
          , h(cons(X, Y)) -> h(g(cons(X, Y)))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 1
        , s_0(2) -> 2
        , s_1(2) -> 1
        , s_1(2) -> 3
        , g_0(2) -> 1
        , g_1(2) -> 1
        , g_1(2) -> 3
        , g_1(4) -> 3
        , cons_0(2, 2) -> 2
        , cons_1(2, 2) -> 4
        , 0_0() -> 2
        , h_0(2) -> 1
        , h_1(3) -> 1}

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed innermost test830

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Mixed innermost test830

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  f(s(X)) -> f(X)
     , g(cons(0(), Y)) -> g(Y)
     , g(cons(s(X), Y)) -> s(X)
     , h(cons(X, Y)) -> h(g(cons(X, Y)))}

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:
         {  f(s(X)) -> f(X)
          , g(cons(0(), Y)) -> g(Y)
          , g(cons(s(X), Y)) -> s(X)
          , h(cons(X, Y)) -> h(g(cons(X, Y)))}

     Proof Output:
       The problem is match-bounded by 1.
       The enriched problem is compatible with the following automaton:
       {  f_0(2) -> 1
        , f_1(2) -> 1
        , s_0(2) -> 2
        , s_1(2) -> 1
        , s_1(2) -> 3
        , g_0(2) -> 1
        , g_1(2) -> 1
        , g_1(2) -> 3
        , g_1(4) -> 3
        , cons_0(2, 2) -> 2
        , cons_1(2, 2) -> 4
        , 0_0() -> 2
        , h_0(2) -> 1
        , h_1(3) -> 1}