MAYBE

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

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


Arrrr..