MAYBE

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

Strict Trs:
  { half(0()) -> 0()
  , half(s(0())) -> 0()
  , half(s(s(x))) -> s(half(x))
  , lastbit(0()) -> 0()
  , lastbit(s(0())) -> s(0())
  , lastbit(s(s(x))) -> lastbit(x)
  , conv(0()) -> cons(nil(), 0())
  , conv(s(x)) -> cons(conv(half(s(x))), lastbit(s(x))) }
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) '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
      
      2) '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
      
   
   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^#(0()) -> c_1()
     , half^#(s(0())) -> c_2()
     , half^#(s(s(x))) -> c_3(half^#(x))
     , lastbit^#(0()) -> c_4()
     , lastbit^#(s(0())) -> c_5()
     , lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
     , conv^#(0()) -> c_7()
     , conv^#(s(x)) -> c_8(conv^#(half(s(x))), lastbit^#(s(x))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { half^#(0()) -> c_1()
     , half^#(s(0())) -> c_2()
     , half^#(s(s(x))) -> c_3(half^#(x))
     , lastbit^#(0()) -> c_4()
     , lastbit^#(s(0())) -> c_5()
     , lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
     , conv^#(0()) -> c_7()
     , conv^#(s(x)) -> c_8(conv^#(half(s(x))), lastbit^#(s(x))) }
   Strict Trs:
     { half(0()) -> 0()
     , half(s(0())) -> 0()
     , half(s(s(x))) -> s(half(x))
     , lastbit(0()) -> 0()
     , lastbit(s(0())) -> s(0())
     , lastbit(s(s(x))) -> lastbit(x)
     , conv(0()) -> cons(nil(), 0())
     , conv(s(x)) -> cons(conv(half(s(x))), lastbit(s(x))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,4,5,7} by
   applications of Pre({1,2,4,5,7}) = {3,6,8}. Here rules are labeled
   as follows:
   
     DPs:
       { 1: half^#(0()) -> c_1()
       , 2: half^#(s(0())) -> c_2()
       , 3: half^#(s(s(x))) -> c_3(half^#(x))
       , 4: lastbit^#(0()) -> c_4()
       , 5: lastbit^#(s(0())) -> c_5()
       , 6: lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
       , 7: conv^#(0()) -> c_7()
       , 8: conv^#(s(x)) -> c_8(conv^#(half(s(x))), lastbit^#(s(x))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { half^#(s(s(x))) -> c_3(half^#(x))
     , lastbit^#(s(s(x))) -> c_6(lastbit^#(x))
     , conv^#(s(x)) -> c_8(conv^#(half(s(x))), lastbit^#(s(x))) }
   Strict Trs:
     { half(0()) -> 0()
     , half(s(0())) -> 0()
     , half(s(s(x))) -> s(half(x))
     , lastbit(0()) -> 0()
     , lastbit(s(0())) -> s(0())
     , lastbit(s(s(x))) -> lastbit(x)
     , conv(0()) -> cons(nil(), 0())
     , conv(s(x)) -> cons(conv(half(s(x))), lastbit(s(x))) }
   Weak DPs:
     { half^#(0()) -> c_1()
     , half^#(s(0())) -> c_2()
     , lastbit^#(0()) -> c_4()
     , lastbit^#(s(0())) -> c_5()
     , conv^#(0()) -> c_7() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..