MAYBE

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

Strict Trs:
  { ge(x, 0()) -> true()
  , ge(0(), s(y)) -> false()
  , ge(s(x), s(y)) -> ge(x, y)
  , minus(x, 0()) -> x
  , minus(0(), y) -> 0()
  , minus(s(x), s(y)) -> minus(x, y)
  , id_inc(x) -> x
  , id_inc(x) -> s(x)
  , div(x, y) -> if(ge(y, s(0())), ge(x, y), x, y)
  , if(true(), true(), x, y) -> id_inc(div(minus(x, y), y))
  , if(true(), false(), x, y) -> 0()
  , if(false(), b, x, y) -> div_by_zero() }
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:
     { ge^#(x, 0()) -> c_1()
     , ge^#(0(), s(y)) -> c_2()
     , ge^#(s(x), s(y)) -> c_3(ge^#(x, y))
     , minus^#(x, 0()) -> c_4(x)
     , minus^#(0(), y) -> c_5()
     , minus^#(s(x), s(y)) -> c_6(minus^#(x, y))
     , id_inc^#(x) -> c_7(x)
     , id_inc^#(x) -> c_8(x)
     , div^#(x, y) -> c_9(if^#(ge(y, s(0())), ge(x, y), x, y))
     , if^#(true(), true(), x, y) -> c_10(id_inc^#(div(minus(x, y), y)))
     , if^#(true(), false(), x, y) -> c_11()
     , if^#(false(), b, x, y) -> c_12() }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { ge^#(x, 0()) -> c_1()
     , ge^#(0(), s(y)) -> c_2()
     , ge^#(s(x), s(y)) -> c_3(ge^#(x, y))
     , minus^#(x, 0()) -> c_4(x)
     , minus^#(0(), y) -> c_5()
     , minus^#(s(x), s(y)) -> c_6(minus^#(x, y))
     , id_inc^#(x) -> c_7(x)
     , id_inc^#(x) -> c_8(x)
     , div^#(x, y) -> c_9(if^#(ge(y, s(0())), ge(x, y), x, y))
     , if^#(true(), true(), x, y) -> c_10(id_inc^#(div(minus(x, y), y)))
     , if^#(true(), false(), x, y) -> c_11()
     , if^#(false(), b, x, y) -> c_12() }
   Strict Trs:
     { ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , minus(x, 0()) -> x
     , minus(0(), y) -> 0()
     , minus(s(x), s(y)) -> minus(x, y)
     , id_inc(x) -> x
     , id_inc(x) -> s(x)
     , div(x, y) -> if(ge(y, s(0())), ge(x, y), x, y)
     , if(true(), true(), x, y) -> id_inc(div(minus(x, y), y))
     , if(true(), false(), x, y) -> 0()
     , if(false(), b, x, y) -> div_by_zero() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,5,11,12} by
   applications of Pre({1,2,5,11,12}) = {3,4,6,7,8,9}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: ge^#(x, 0()) -> c_1()
       , 2: ge^#(0(), s(y)) -> c_2()
       , 3: ge^#(s(x), s(y)) -> c_3(ge^#(x, y))
       , 4: minus^#(x, 0()) -> c_4(x)
       , 5: minus^#(0(), y) -> c_5()
       , 6: minus^#(s(x), s(y)) -> c_6(minus^#(x, y))
       , 7: id_inc^#(x) -> c_7(x)
       , 8: id_inc^#(x) -> c_8(x)
       , 9: div^#(x, y) -> c_9(if^#(ge(y, s(0())), ge(x, y), x, y))
       , 10: if^#(true(), true(), x, y) ->
             c_10(id_inc^#(div(minus(x, y), y)))
       , 11: if^#(true(), false(), x, y) -> c_11()
       , 12: if^#(false(), b, x, y) -> c_12() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { ge^#(s(x), s(y)) -> c_3(ge^#(x, y))
     , minus^#(x, 0()) -> c_4(x)
     , minus^#(s(x), s(y)) -> c_6(minus^#(x, y))
     , id_inc^#(x) -> c_7(x)
     , id_inc^#(x) -> c_8(x)
     , div^#(x, y) -> c_9(if^#(ge(y, s(0())), ge(x, y), x, y))
     , if^#(true(), true(), x, y) ->
       c_10(id_inc^#(div(minus(x, y), y))) }
   Strict Trs:
     { ge(x, 0()) -> true()
     , ge(0(), s(y)) -> false()
     , ge(s(x), s(y)) -> ge(x, y)
     , minus(x, 0()) -> x
     , minus(0(), y) -> 0()
     , minus(s(x), s(y)) -> minus(x, y)
     , id_inc(x) -> x
     , id_inc(x) -> s(x)
     , div(x, y) -> if(ge(y, s(0())), ge(x, y), x, y)
     , if(true(), true(), x, y) -> id_inc(div(minus(x, y), y))
     , if(true(), false(), x, y) -> 0()
     , if(false(), b, x, y) -> div_by_zero() }
   Weak DPs:
     { ge^#(x, 0()) -> c_1()
     , ge^#(0(), s(y)) -> c_2()
     , minus^#(0(), y) -> c_5()
     , if^#(true(), false(), x, y) -> c_11()
     , if^#(false(), b, x, y) -> c_12() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..