MAYBE

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

Strict Trs:
  { times(x, y) -> sum(generate(x, y))
  , sum(nil()) -> 0()
  , sum(cons(0(), xs)) -> sum(xs)
  , sum(cons(s(x), xs)) -> s(sum(cons(x, xs)))
  , generate(x, y) -> gen(x, y, 0())
  , gen(x, y, z) -> if(ge(z, x), x, y, z)
  , if(true(), x, y, z) -> nil()
  , if(false(), x, y, z) -> cons(y, gen(x, y, s(z)))
  , ge(x, 0()) -> true()
  , ge(0(), s(y)) -> false()
  , ge(s(x), s(y)) -> ge(x, 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) '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
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { times^#(x, y) -> c_1(sum^#(generate(x, y)))
     , sum^#(nil()) -> c_2()
     , sum^#(cons(0(), xs)) -> c_3(sum^#(xs))
     , sum^#(cons(s(x), xs)) -> c_4(sum^#(cons(x, xs)))
     , generate^#(x, y) -> c_5(gen^#(x, y, 0()))
     , gen^#(x, y, z) -> c_6(if^#(ge(z, x), x, y, z))
     , if^#(true(), x, y, z) -> c_7()
     , if^#(false(), x, y, z) -> c_8(y, gen^#(x, y, s(z)))
     , ge^#(x, 0()) -> c_9()
     , ge^#(0(), s(y)) -> c_10()
     , ge^#(s(x), s(y)) -> c_11(ge^#(x, y)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { times^#(x, y) -> c_1(sum^#(generate(x, y)))
     , sum^#(nil()) -> c_2()
     , sum^#(cons(0(), xs)) -> c_3(sum^#(xs))
     , sum^#(cons(s(x), xs)) -> c_4(sum^#(cons(x, xs)))
     , generate^#(x, y) -> c_5(gen^#(x, y, 0()))
     , gen^#(x, y, z) -> c_6(if^#(ge(z, x), x, y, z))
     , if^#(true(), x, y, z) -> c_7()
     , if^#(false(), x, y, z) -> c_8(y, gen^#(x, y, s(z)))
     , ge^#(x, 0()) -> c_9()
     , ge^#(0(), s(y)) -> c_10()
     , ge^#(s(x), s(y)) -> c_11(ge^#(x, y)) }
   Strict Trs:
     { times(x, y) -> sum(generate(x, y))
     , sum(nil()) -> 0()
     , sum(cons(0(), xs)) -> sum(xs)
     , sum(cons(s(x), xs)) -> s(sum(cons(x, xs)))
     , generate(x, y) -> gen(x, y, 0())
     , gen(x, y, z) -> if(ge(z, x), x, y, z)
     , if(true(), x, y, z) -> nil()
     , if(false(), x, y, z) -> cons(y, gen(x, y, s(z)))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2,7,9,10} by applications
   of Pre({2,7,9,10}) = {1,3,6,8,11}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: times^#(x, y) -> c_1(sum^#(generate(x, y)))
       , 2: sum^#(nil()) -> c_2()
       , 3: sum^#(cons(0(), xs)) -> c_3(sum^#(xs))
       , 4: sum^#(cons(s(x), xs)) -> c_4(sum^#(cons(x, xs)))
       , 5: generate^#(x, y) -> c_5(gen^#(x, y, 0()))
       , 6: gen^#(x, y, z) -> c_6(if^#(ge(z, x), x, y, z))
       , 7: if^#(true(), x, y, z) -> c_7()
       , 8: if^#(false(), x, y, z) -> c_8(y, gen^#(x, y, s(z)))
       , 9: ge^#(x, 0()) -> c_9()
       , 10: ge^#(0(), s(y)) -> c_10()
       , 11: ge^#(s(x), s(y)) -> c_11(ge^#(x, y)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { times^#(x, y) -> c_1(sum^#(generate(x, y)))
     , sum^#(cons(0(), xs)) -> c_3(sum^#(xs))
     , sum^#(cons(s(x), xs)) -> c_4(sum^#(cons(x, xs)))
     , generate^#(x, y) -> c_5(gen^#(x, y, 0()))
     , gen^#(x, y, z) -> c_6(if^#(ge(z, x), x, y, z))
     , if^#(false(), x, y, z) -> c_8(y, gen^#(x, y, s(z)))
     , ge^#(s(x), s(y)) -> c_11(ge^#(x, y)) }
   Strict Trs:
     { times(x, y) -> sum(generate(x, y))
     , sum(nil()) -> 0()
     , sum(cons(0(), xs)) -> sum(xs)
     , sum(cons(s(x), xs)) -> s(sum(cons(x, xs)))
     , generate(x, y) -> gen(x, y, 0())
     , gen(x, y, z) -> if(ge(z, x), x, y, z)
     , if(true(), x, y, z) -> nil()
     , if(false(), x, y, z) -> cons(y, gen(x, y, s(z)))
     , ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y) }
   Weak DPs:
     { sum^#(nil()) -> c_2()
     , if^#(true(), x, y, z) -> c_7()
     , ge^#(x, 0()) -> c_9()
     , ge^#(0(), s(y)) -> c_10() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..