MAYBE

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

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


Arrrr..