MAYBE

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

Strict Trs:
  { half(x) -> if(ge(x, s(s(0()))), x)
  , if(false(), x) -> 0()
  , if(true(), x) -> s(half(p(p(x))))
  , ge(x, 0()) -> true()
  , ge(s(x), s(y)) -> ge(x, y)
  , ge(0(), s(x)) -> false()
  , p(s(x)) -> x
  , p(0()) -> 0()
  , log(s(x)) -> s(log(half(s(x))))
  , log(0()) -> 0() }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) '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.
      
   

2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { half^#(x) -> c_1(if^#(ge(x, s(s(0()))), x))
     , if^#(false(), x) -> c_2()
     , if^#(true(), x) -> c_3(half^#(p(p(x))))
     , ge^#(x, 0()) -> c_4()
     , ge^#(s(x), s(y)) -> c_5(ge^#(x, y))
     , ge^#(0(), s(x)) -> c_6()
     , p^#(s(x)) -> c_7(x)
     , p^#(0()) -> c_8()
     , log^#(s(x)) -> c_9(log^#(half(s(x))))
     , log^#(0()) -> c_10() }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { half^#(x) -> c_1(if^#(ge(x, s(s(0()))), x))
     , if^#(false(), x) -> c_2()
     , if^#(true(), x) -> c_3(half^#(p(p(x))))
     , ge^#(x, 0()) -> c_4()
     , ge^#(s(x), s(y)) -> c_5(ge^#(x, y))
     , ge^#(0(), s(x)) -> c_6()
     , p^#(s(x)) -> c_7(x)
     , p^#(0()) -> c_8()
     , log^#(s(x)) -> c_9(log^#(half(s(x))))
     , log^#(0()) -> c_10() }
   Strict Trs:
     { half(x) -> if(ge(x, s(s(0()))), x)
     , if(false(), x) -> 0()
     , if(true(), x) -> s(half(p(p(x))))
     , ge(x, 0()) -> true()
     , ge(s(x), s(y)) -> ge(x, y)
     , ge(0(), s(x)) -> false()
     , p(s(x)) -> x
     , p(0()) -> 0()
     , log(s(x)) -> s(log(half(s(x))))
     , log(0()) -> 0() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2,4,6,8,10} by
   applications of Pre({2,4,6,8,10}) = {1,5,7,9}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: half^#(x) -> c_1(if^#(ge(x, s(s(0()))), x))
       , 2: if^#(false(), x) -> c_2()
       , 3: if^#(true(), x) -> c_3(half^#(p(p(x))))
       , 4: ge^#(x, 0()) -> c_4()
       , 5: ge^#(s(x), s(y)) -> c_5(ge^#(x, y))
       , 6: ge^#(0(), s(x)) -> c_6()
       , 7: p^#(s(x)) -> c_7(x)
       , 8: p^#(0()) -> c_8()
       , 9: log^#(s(x)) -> c_9(log^#(half(s(x))))
       , 10: log^#(0()) -> c_10() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { half^#(x) -> c_1(if^#(ge(x, s(s(0()))), x))
     , if^#(true(), x) -> c_3(half^#(p(p(x))))
     , ge^#(s(x), s(y)) -> c_5(ge^#(x, y))
     , p^#(s(x)) -> c_7(x)
     , log^#(s(x)) -> c_9(log^#(half(s(x)))) }
   Strict Trs:
     { half(x) -> if(ge(x, s(s(0()))), x)
     , if(false(), x) -> 0()
     , if(true(), x) -> s(half(p(p(x))))
     , ge(x, 0()) -> true()
     , ge(s(x), s(y)) -> ge(x, y)
     , ge(0(), s(x)) -> false()
     , p(s(x)) -> x
     , p(0()) -> 0()
     , log(s(x)) -> s(log(half(s(x))))
     , log(0()) -> 0() }
   Weak DPs:
     { if^#(false(), x) -> c_2()
     , ge^#(x, 0()) -> c_4()
     , ge^#(0(), s(x)) -> c_6()
     , p^#(0()) -> c_8()
     , log^#(0()) -> c_10() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..