MAYBE

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

Strict Trs:
  { -(x, 0()) -> x
  , -(0(), s(y)) -> 0()
  , -(s(x), s(y)) -> -(x, y)
  , lt(x, 0()) -> false()
  , lt(0(), s(y)) -> true()
  , lt(s(x), s(y)) -> lt(x, y)
  , if(false(), x, y) -> y
  , if(true(), x, y) -> x
  , div(x, 0()) -> 0()
  , div(0(), y) -> 0()
  , div(s(x), s(y)) -> if(lt(x, y), 0(), s(div(-(x, y), 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:
     { -^#(x, 0()) -> c_1(x)
     , -^#(0(), s(y)) -> c_2()
     , -^#(s(x), s(y)) -> c_3(-^#(x, y))
     , lt^#(x, 0()) -> c_4()
     , lt^#(0(), s(y)) -> c_5()
     , lt^#(s(x), s(y)) -> c_6(lt^#(x, y))
     , if^#(false(), x, y) -> c_7(y)
     , if^#(true(), x, y) -> c_8(x)
     , div^#(x, 0()) -> c_9()
     , div^#(0(), y) -> c_10()
     , div^#(s(x), s(y)) ->
       c_11(if^#(lt(x, y), 0(), s(div(-(x, y), s(y))))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { -^#(x, 0()) -> c_1(x)
     , -^#(0(), s(y)) -> c_2()
     , -^#(s(x), s(y)) -> c_3(-^#(x, y))
     , lt^#(x, 0()) -> c_4()
     , lt^#(0(), s(y)) -> c_5()
     , lt^#(s(x), s(y)) -> c_6(lt^#(x, y))
     , if^#(false(), x, y) -> c_7(y)
     , if^#(true(), x, y) -> c_8(x)
     , div^#(x, 0()) -> c_9()
     , div^#(0(), y) -> c_10()
     , div^#(s(x), s(y)) ->
       c_11(if^#(lt(x, y), 0(), s(div(-(x, y), s(y))))) }
   Strict Trs:
     { -(x, 0()) -> x
     , -(0(), s(y)) -> 0()
     , -(s(x), s(y)) -> -(x, y)
     , lt(x, 0()) -> false()
     , lt(0(), s(y)) -> true()
     , lt(s(x), s(y)) -> lt(x, y)
     , if(false(), x, y) -> y
     , if(true(), x, y) -> x
     , div(x, 0()) -> 0()
     , div(0(), y) -> 0()
     , div(s(x), s(y)) -> if(lt(x, y), 0(), s(div(-(x, y), s(y)))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2,4,5,9,10} by
   applications of Pre({2,4,5,9,10}) = {1,3,6,7,8}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: -^#(x, 0()) -> c_1(x)
       , 2: -^#(0(), s(y)) -> c_2()
       , 3: -^#(s(x), s(y)) -> c_3(-^#(x, y))
       , 4: lt^#(x, 0()) -> c_4()
       , 5: lt^#(0(), s(y)) -> c_5()
       , 6: lt^#(s(x), s(y)) -> c_6(lt^#(x, y))
       , 7: if^#(false(), x, y) -> c_7(y)
       , 8: if^#(true(), x, y) -> c_8(x)
       , 9: div^#(x, 0()) -> c_9()
       , 10: div^#(0(), y) -> c_10()
       , 11: div^#(s(x), s(y)) ->
             c_11(if^#(lt(x, y), 0(), s(div(-(x, y), s(y))))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { -^#(x, 0()) -> c_1(x)
     , -^#(s(x), s(y)) -> c_3(-^#(x, y))
     , lt^#(s(x), s(y)) -> c_6(lt^#(x, y))
     , if^#(false(), x, y) -> c_7(y)
     , if^#(true(), x, y) -> c_8(x)
     , div^#(s(x), s(y)) ->
       c_11(if^#(lt(x, y), 0(), s(div(-(x, y), s(y))))) }
   Strict Trs:
     { -(x, 0()) -> x
     , -(0(), s(y)) -> 0()
     , -(s(x), s(y)) -> -(x, y)
     , lt(x, 0()) -> false()
     , lt(0(), s(y)) -> true()
     , lt(s(x), s(y)) -> lt(x, y)
     , if(false(), x, y) -> y
     , if(true(), x, y) -> x
     , div(x, 0()) -> 0()
     , div(0(), y) -> 0()
     , div(s(x), s(y)) -> if(lt(x, y), 0(), s(div(-(x, y), s(y)))) }
   Weak DPs:
     { -^#(0(), s(y)) -> c_2()
     , lt^#(x, 0()) -> c_4()
     , lt^#(0(), s(y)) -> c_5()
     , div^#(x, 0()) -> c_9()
     , div^#(0(), y) -> c_10() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..