MAYBE

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

Strict Trs:
  { ge(0(), 0()) -> true()
  , ge(0(), s(0())) -> false()
  , ge(0(), s(s(x))) -> ge(0(), s(x))
  , ge(s(x), 0()) -> ge(x, 0())
  , ge(s(x), s(y)) -> ge(x, y)
  , minus(0(), 0()) -> 0()
  , minus(0(), s(x)) -> minus(0(), x)
  , minus(s(x), 0()) -> s(minus(x, 0()))
  , minus(s(x), s(y)) -> minus(x, y)
  , plus(0(), 0()) -> 0()
  , plus(0(), s(x)) -> s(plus(0(), x))
  , plus(s(x), y) -> s(plus(x, y))
  , div(x, y) -> ify(ge(y, s(0())), x, y)
  , div(plus(x, y), z) -> plus(div(x, z), div(y, z))
  , ify(true(), x, y) -> if(ge(x, y), x, y)
  , ify(false(), x, y) -> divByZeroError()
  , if(true(), x, y) -> s(div(minus(x, y), y))
  , if(false(), x, y) -> 0() }
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^#(0(), 0()) -> c_1()
     , ge^#(0(), s(0())) -> c_2()
     , ge^#(0(), s(s(x))) -> c_3(ge^#(0(), s(x)))
     , ge^#(s(x), 0()) -> c_4(ge^#(x, 0()))
     , ge^#(s(x), s(y)) -> c_5(ge^#(x, y))
     , minus^#(0(), 0()) -> c_6()
     , minus^#(0(), s(x)) -> c_7(minus^#(0(), x))
     , minus^#(s(x), 0()) -> c_8(minus^#(x, 0()))
     , minus^#(s(x), s(y)) -> c_9(minus^#(x, y))
     , plus^#(0(), 0()) -> c_10()
     , plus^#(0(), s(x)) -> c_11(plus^#(0(), x))
     , plus^#(s(x), y) -> c_12(plus^#(x, y))
     , div^#(x, y) -> c_13(ify^#(ge(y, s(0())), x, y))
     , div^#(plus(x, y), z) -> c_14(plus^#(div(x, z), div(y, z)))
     , ify^#(true(), x, y) -> c_15(if^#(ge(x, y), x, y))
     , ify^#(false(), x, y) -> c_16()
     , if^#(true(), x, y) -> c_17(div^#(minus(x, y), y))
     , if^#(false(), x, y) -> c_18() }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { ge^#(0(), 0()) -> c_1()
     , ge^#(0(), s(0())) -> c_2()
     , ge^#(0(), s(s(x))) -> c_3(ge^#(0(), s(x)))
     , ge^#(s(x), 0()) -> c_4(ge^#(x, 0()))
     , ge^#(s(x), s(y)) -> c_5(ge^#(x, y))
     , minus^#(0(), 0()) -> c_6()
     , minus^#(0(), s(x)) -> c_7(minus^#(0(), x))
     , minus^#(s(x), 0()) -> c_8(minus^#(x, 0()))
     , minus^#(s(x), s(y)) -> c_9(minus^#(x, y))
     , plus^#(0(), 0()) -> c_10()
     , plus^#(0(), s(x)) -> c_11(plus^#(0(), x))
     , plus^#(s(x), y) -> c_12(plus^#(x, y))
     , div^#(x, y) -> c_13(ify^#(ge(y, s(0())), x, y))
     , div^#(plus(x, y), z) -> c_14(plus^#(div(x, z), div(y, z)))
     , ify^#(true(), x, y) -> c_15(if^#(ge(x, y), x, y))
     , ify^#(false(), x, y) -> c_16()
     , if^#(true(), x, y) -> c_17(div^#(minus(x, y), y))
     , if^#(false(), x, y) -> c_18() }
   Strict Trs:
     { ge(0(), 0()) -> true()
     , ge(0(), s(0())) -> false()
     , ge(0(), s(s(x))) -> ge(0(), s(x))
     , ge(s(x), 0()) -> ge(x, 0())
     , ge(s(x), s(y)) -> ge(x, y)
     , minus(0(), 0()) -> 0()
     , minus(0(), s(x)) -> minus(0(), x)
     , minus(s(x), 0()) -> s(minus(x, 0()))
     , minus(s(x), s(y)) -> minus(x, y)
     , plus(0(), 0()) -> 0()
     , plus(0(), s(x)) -> s(plus(0(), x))
     , plus(s(x), y) -> s(plus(x, y))
     , div(x, y) -> ify(ge(y, s(0())), x, y)
     , div(plus(x, y), z) -> plus(div(x, z), div(y, z))
     , ify(true(), x, y) -> if(ge(x, y), x, y)
     , ify(false(), x, y) -> divByZeroError()
     , if(true(), x, y) -> s(div(minus(x, y), y))
     , if(false(), x, y) -> 0() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,6,10,16,18} by
   applications of Pre({1,2,6,10,16,18}) =
   {3,4,5,7,8,9,11,12,13,14,15}. Here rules are labeled as follows:
   
     DPs:
       { 1: ge^#(0(), 0()) -> c_1()
       , 2: ge^#(0(), s(0())) -> c_2()
       , 3: ge^#(0(), s(s(x))) -> c_3(ge^#(0(), s(x)))
       , 4: ge^#(s(x), 0()) -> c_4(ge^#(x, 0()))
       , 5: ge^#(s(x), s(y)) -> c_5(ge^#(x, y))
       , 6: minus^#(0(), 0()) -> c_6()
       , 7: minus^#(0(), s(x)) -> c_7(minus^#(0(), x))
       , 8: minus^#(s(x), 0()) -> c_8(minus^#(x, 0()))
       , 9: minus^#(s(x), s(y)) -> c_9(minus^#(x, y))
       , 10: plus^#(0(), 0()) -> c_10()
       , 11: plus^#(0(), s(x)) -> c_11(plus^#(0(), x))
       , 12: plus^#(s(x), y) -> c_12(plus^#(x, y))
       , 13: div^#(x, y) -> c_13(ify^#(ge(y, s(0())), x, y))
       , 14: div^#(plus(x, y), z) -> c_14(plus^#(div(x, z), div(y, z)))
       , 15: ify^#(true(), x, y) -> c_15(if^#(ge(x, y), x, y))
       , 16: ify^#(false(), x, y) -> c_16()
       , 17: if^#(true(), x, y) -> c_17(div^#(minus(x, y), y))
       , 18: if^#(false(), x, y) -> c_18() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { ge^#(0(), s(s(x))) -> c_3(ge^#(0(), s(x)))
     , ge^#(s(x), 0()) -> c_4(ge^#(x, 0()))
     , ge^#(s(x), s(y)) -> c_5(ge^#(x, y))
     , minus^#(0(), s(x)) -> c_7(minus^#(0(), x))
     , minus^#(s(x), 0()) -> c_8(minus^#(x, 0()))
     , minus^#(s(x), s(y)) -> c_9(minus^#(x, y))
     , plus^#(0(), s(x)) -> c_11(plus^#(0(), x))
     , plus^#(s(x), y) -> c_12(plus^#(x, y))
     , div^#(x, y) -> c_13(ify^#(ge(y, s(0())), x, y))
     , div^#(plus(x, y), z) -> c_14(plus^#(div(x, z), div(y, z)))
     , ify^#(true(), x, y) -> c_15(if^#(ge(x, y), x, y))
     , if^#(true(), x, y) -> c_17(div^#(minus(x, y), y)) }
   Strict Trs:
     { ge(0(), 0()) -> true()
     , ge(0(), s(0())) -> false()
     , ge(0(), s(s(x))) -> ge(0(), s(x))
     , ge(s(x), 0()) -> ge(x, 0())
     , ge(s(x), s(y)) -> ge(x, y)
     , minus(0(), 0()) -> 0()
     , minus(0(), s(x)) -> minus(0(), x)
     , minus(s(x), 0()) -> s(minus(x, 0()))
     , minus(s(x), s(y)) -> minus(x, y)
     , plus(0(), 0()) -> 0()
     , plus(0(), s(x)) -> s(plus(0(), x))
     , plus(s(x), y) -> s(plus(x, y))
     , div(x, y) -> ify(ge(y, s(0())), x, y)
     , div(plus(x, y), z) -> plus(div(x, z), div(y, z))
     , ify(true(), x, y) -> if(ge(x, y), x, y)
     , ify(false(), x, y) -> divByZeroError()
     , if(true(), x, y) -> s(div(minus(x, y), y))
     , if(false(), x, y) -> 0() }
   Weak DPs:
     { ge^#(0(), 0()) -> c_1()
     , ge^#(0(), s(0())) -> c_2()
     , minus^#(0(), 0()) -> c_6()
     , plus^#(0(), 0()) -> c_10()
     , ify^#(false(), x, y) -> c_16()
     , if^#(false(), x, y) -> c_18() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..