MAYBE

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

Strict Trs:
  { 1024() -> 1024_1(0())
  , 1024_1(x) -> if(lt(x, 10()), x)
  , if(true(), x) -> double(1024_1(s(x)))
  , if(false(), x) -> s(0())
  , lt(x, 0()) -> false()
  , lt(0(), s(y)) -> true()
  , lt(s(x), s(y)) -> lt(x, y)
  , 10() -> double(s(double(s(s(0())))))
  , double(0()) -> 0()
  , double(s(x)) -> s(s(double(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) '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 minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   
   3) '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
      
   

2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { 1024^#() -> c_1(1024_1^#(0()))
     , 1024_1^#(x) -> c_2(if^#(lt(x, 10()), x))
     , if^#(true(), x) -> c_3(double^#(1024_1(s(x))))
     , if^#(false(), x) -> c_4()
     , double^#(0()) -> c_9()
     , double^#(s(x)) -> c_10(double^#(x))
     , lt^#(x, 0()) -> c_5()
     , lt^#(0(), s(y)) -> c_6()
     , lt^#(s(x), s(y)) -> c_7(lt^#(x, y))
     , 10^#() -> c_8(double^#(s(double(s(s(0())))))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { 1024^#() -> c_1(1024_1^#(0()))
     , 1024_1^#(x) -> c_2(if^#(lt(x, 10()), x))
     , if^#(true(), x) -> c_3(double^#(1024_1(s(x))))
     , if^#(false(), x) -> c_4()
     , double^#(0()) -> c_9()
     , double^#(s(x)) -> c_10(double^#(x))
     , lt^#(x, 0()) -> c_5()
     , lt^#(0(), s(y)) -> c_6()
     , lt^#(s(x), s(y)) -> c_7(lt^#(x, y))
     , 10^#() -> c_8(double^#(s(double(s(s(0())))))) }
   Strict Trs:
     { 1024() -> 1024_1(0())
     , 1024_1(x) -> if(lt(x, 10()), x)
     , if(true(), x) -> double(1024_1(s(x)))
     , if(false(), x) -> s(0())
     , lt(x, 0()) -> false()
     , lt(0(), s(y)) -> true()
     , lt(s(x), s(y)) -> lt(x, y)
     , 10() -> double(s(double(s(s(0())))))
     , double(0()) -> 0()
     , double(s(x)) -> s(s(double(x))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {4,5,7,8} by applications
   of Pre({4,5,7,8}) = {2,3,6,9}. Here rules are labeled as follows:
   
     DPs:
       { 1: 1024^#() -> c_1(1024_1^#(0()))
       , 2: 1024_1^#(x) -> c_2(if^#(lt(x, 10()), x))
       , 3: if^#(true(), x) -> c_3(double^#(1024_1(s(x))))
       , 4: if^#(false(), x) -> c_4()
       , 5: double^#(0()) -> c_9()
       , 6: double^#(s(x)) -> c_10(double^#(x))
       , 7: lt^#(x, 0()) -> c_5()
       , 8: lt^#(0(), s(y)) -> c_6()
       , 9: lt^#(s(x), s(y)) -> c_7(lt^#(x, y))
       , 10: 10^#() -> c_8(double^#(s(double(s(s(0())))))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { 1024^#() -> c_1(1024_1^#(0()))
     , 1024_1^#(x) -> c_2(if^#(lt(x, 10()), x))
     , if^#(true(), x) -> c_3(double^#(1024_1(s(x))))
     , double^#(s(x)) -> c_10(double^#(x))
     , lt^#(s(x), s(y)) -> c_7(lt^#(x, y))
     , 10^#() -> c_8(double^#(s(double(s(s(0())))))) }
   Strict Trs:
     { 1024() -> 1024_1(0())
     , 1024_1(x) -> if(lt(x, 10()), x)
     , if(true(), x) -> double(1024_1(s(x)))
     , if(false(), x) -> s(0())
     , lt(x, 0()) -> false()
     , lt(0(), s(y)) -> true()
     , lt(s(x), s(y)) -> lt(x, y)
     , 10() -> double(s(double(s(s(0())))))
     , double(0()) -> 0()
     , double(s(x)) -> s(s(double(x))) }
   Weak DPs:
     { if^#(false(), x) -> c_4()
     , double^#(0()) -> c_9()
     , lt^#(x, 0()) -> c_5()
     , lt^#(0(), s(y)) -> c_6() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..