MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { p(0()) -> 0()
  , p(s(x)) -> x
  , minus(x, 0()) -> x
  , minus(x, s(y)) -> p(minus(x, y))
  , minus(s(x), s(y)) -> minus(x, y)
  , div(0(), s(y)) -> 0()
  , div(s(x), s(y)) -> s(div(minus(s(x), s(y)), s(y)))
  , log(s(0()), s(s(y))) -> 0()
  , log(s(s(x)), s(s(y))) ->
    s(log(div(minus(x, y), s(s(y))), s(s(y)))) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      Computation stopped due to timeout after 30.0 seconds.
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { p^#(0()) -> c_1()
     , p^#(s(x)) -> c_2(x)
     , minus^#(x, 0()) -> c_3(x)
     , minus^#(x, s(y)) -> c_4(p^#(minus(x, y)))
     , minus^#(s(x), s(y)) -> c_5(minus^#(x, y))
     , div^#(0(), s(y)) -> c_6()
     , div^#(s(x), s(y)) -> c_7(div^#(minus(s(x), s(y)), s(y)))
     , log^#(s(0()), s(s(y))) -> c_8()
     , log^#(s(s(x)), s(s(y))) ->
       c_9(log^#(div(minus(x, y), s(s(y))), s(s(y)))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { p^#(0()) -> c_1()
     , p^#(s(x)) -> c_2(x)
     , minus^#(x, 0()) -> c_3(x)
     , minus^#(x, s(y)) -> c_4(p^#(minus(x, y)))
     , minus^#(s(x), s(y)) -> c_5(minus^#(x, y))
     , div^#(0(), s(y)) -> c_6()
     , div^#(s(x), s(y)) -> c_7(div^#(minus(s(x), s(y)), s(y)))
     , log^#(s(0()), s(s(y))) -> c_8()
     , log^#(s(s(x)), s(s(y))) ->
       c_9(log^#(div(minus(x, y), s(s(y))), s(s(y)))) }
   Strict Trs:
     { p(0()) -> 0()
     , p(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> p(minus(x, y))
     , minus(s(x), s(y)) -> minus(x, y)
     , div(0(), s(y)) -> 0()
     , div(s(x), s(y)) -> s(div(minus(s(x), s(y)), s(y)))
     , log(s(0()), s(s(y))) -> 0()
     , log(s(s(x)), s(s(y))) ->
       s(log(div(minus(x, y), s(s(y))), s(s(y)))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,6,8} by applications of
   Pre({1,6,8}) = {2,3,4,7,9}. Here rules are labeled as follows:
   
     DPs:
       { 1: p^#(0()) -> c_1()
       , 2: p^#(s(x)) -> c_2(x)
       , 3: minus^#(x, 0()) -> c_3(x)
       , 4: minus^#(x, s(y)) -> c_4(p^#(minus(x, y)))
       , 5: minus^#(s(x), s(y)) -> c_5(minus^#(x, y))
       , 6: div^#(0(), s(y)) -> c_6()
       , 7: div^#(s(x), s(y)) -> c_7(div^#(minus(s(x), s(y)), s(y)))
       , 8: log^#(s(0()), s(s(y))) -> c_8()
       , 9: log^#(s(s(x)), s(s(y))) ->
            c_9(log^#(div(minus(x, y), s(s(y))), s(s(y)))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { p^#(s(x)) -> c_2(x)
     , minus^#(x, 0()) -> c_3(x)
     , minus^#(x, s(y)) -> c_4(p^#(minus(x, y)))
     , minus^#(s(x), s(y)) -> c_5(minus^#(x, y))
     , div^#(s(x), s(y)) -> c_7(div^#(minus(s(x), s(y)), s(y)))
     , log^#(s(s(x)), s(s(y))) ->
       c_9(log^#(div(minus(x, y), s(s(y))), s(s(y)))) }
   Strict Trs:
     { p(0()) -> 0()
     , p(s(x)) -> x
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> p(minus(x, y))
     , minus(s(x), s(y)) -> minus(x, y)
     , div(0(), s(y)) -> 0()
     , div(s(x), s(y)) -> s(div(minus(s(x), s(y)), s(y)))
     , log(s(0()), s(s(y))) -> 0()
     , log(s(s(x)), s(s(y))) ->
       s(log(div(minus(x, y), s(s(y))), s(s(y)))) }
   Weak DPs:
     { p^#(0()) -> c_1()
     , div^#(0(), s(y)) -> c_6()
     , log^#(s(0()), s(s(y))) -> c_8() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..