MAYBE

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

Strict Trs:
  { le(0(), y, z) -> greater(y, z)
  , le(s(x), 0(), z) -> false()
  , le(s(x), s(y), 0()) -> false()
  , le(s(x), s(y), s(z)) -> le(x, y, z)
  , greater(x, 0()) -> first()
  , greater(0(), s(y)) -> second()
  , greater(s(x), s(y)) -> greater(x, y)
  , double(0()) -> 0()
  , double(s(x)) -> s(s(double(x)))
  , triple(x) -> if(le(x, x, double(x)), x, 0(), 0())
  , if(false(), x, y, z) -> true()
  , if(first(), x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
  , if(second(), x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), 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) '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
      
      2) '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
      
   
   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:
     { le^#(0(), y, z) -> c_1(greater^#(y, z))
     , le^#(s(x), 0(), z) -> c_2()
     , le^#(s(x), s(y), 0()) -> c_3()
     , le^#(s(x), s(y), s(z)) -> c_4(le^#(x, y, z))
     , greater^#(x, 0()) -> c_5()
     , greater^#(0(), s(y)) -> c_6()
     , greater^#(s(x), s(y)) -> c_7(greater^#(x, y))
     , double^#(0()) -> c_8()
     , double^#(s(x)) -> c_9(double^#(x))
     , triple^#(x) -> c_10(if^#(le(x, x, double(x)), x, 0(), 0()))
     , if^#(false(), x, y, z) -> c_11()
     , if^#(first(), x, y, z) ->
       c_12(if^#(le(s(x), y, s(z)), s(x), y, s(z)))
     , if^#(second(), x, y, z) ->
       c_13(if^#(le(s(x), s(y), z), s(x), s(y), z)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { le^#(0(), y, z) -> c_1(greater^#(y, z))
     , le^#(s(x), 0(), z) -> c_2()
     , le^#(s(x), s(y), 0()) -> c_3()
     , le^#(s(x), s(y), s(z)) -> c_4(le^#(x, y, z))
     , greater^#(x, 0()) -> c_5()
     , greater^#(0(), s(y)) -> c_6()
     , greater^#(s(x), s(y)) -> c_7(greater^#(x, y))
     , double^#(0()) -> c_8()
     , double^#(s(x)) -> c_9(double^#(x))
     , triple^#(x) -> c_10(if^#(le(x, x, double(x)), x, 0(), 0()))
     , if^#(false(), x, y, z) -> c_11()
     , if^#(first(), x, y, z) ->
       c_12(if^#(le(s(x), y, s(z)), s(x), y, s(z)))
     , if^#(second(), x, y, z) ->
       c_13(if^#(le(s(x), s(y), z), s(x), s(y), z)) }
   Strict Trs:
     { le(0(), y, z) -> greater(y, z)
     , le(s(x), 0(), z) -> false()
     , le(s(x), s(y), 0()) -> false()
     , le(s(x), s(y), s(z)) -> le(x, y, z)
     , greater(x, 0()) -> first()
     , greater(0(), s(y)) -> second()
     , greater(s(x), s(y)) -> greater(x, y)
     , double(0()) -> 0()
     , double(s(x)) -> s(s(double(x)))
     , triple(x) -> if(le(x, x, double(x)), x, 0(), 0())
     , if(false(), x, y, z) -> true()
     , if(first(), x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
     , if(second(), x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2,3,5,6,8,11} by
   applications of Pre({2,3,5,6,8,11}) = {1,4,7,9,10,12,13}. Here
   rules are labeled as follows:
   
     DPs:
       { 1: le^#(0(), y, z) -> c_1(greater^#(y, z))
       , 2: le^#(s(x), 0(), z) -> c_2()
       , 3: le^#(s(x), s(y), 0()) -> c_3()
       , 4: le^#(s(x), s(y), s(z)) -> c_4(le^#(x, y, z))
       , 5: greater^#(x, 0()) -> c_5()
       , 6: greater^#(0(), s(y)) -> c_6()
       , 7: greater^#(s(x), s(y)) -> c_7(greater^#(x, y))
       , 8: double^#(0()) -> c_8()
       , 9: double^#(s(x)) -> c_9(double^#(x))
       , 10: triple^#(x) -> c_10(if^#(le(x, x, double(x)), x, 0(), 0()))
       , 11: if^#(false(), x, y, z) -> c_11()
       , 12: if^#(first(), x, y, z) ->
             c_12(if^#(le(s(x), y, s(z)), s(x), y, s(z)))
       , 13: if^#(second(), x, y, z) ->
             c_13(if^#(le(s(x), s(y), z), s(x), s(y), z)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { le^#(0(), y, z) -> c_1(greater^#(y, z))
     , le^#(s(x), s(y), s(z)) -> c_4(le^#(x, y, z))
     , greater^#(s(x), s(y)) -> c_7(greater^#(x, y))
     , double^#(s(x)) -> c_9(double^#(x))
     , triple^#(x) -> c_10(if^#(le(x, x, double(x)), x, 0(), 0()))
     , if^#(first(), x, y, z) ->
       c_12(if^#(le(s(x), y, s(z)), s(x), y, s(z)))
     , if^#(second(), x, y, z) ->
       c_13(if^#(le(s(x), s(y), z), s(x), s(y), z)) }
   Strict Trs:
     { le(0(), y, z) -> greater(y, z)
     , le(s(x), 0(), z) -> false()
     , le(s(x), s(y), 0()) -> false()
     , le(s(x), s(y), s(z)) -> le(x, y, z)
     , greater(x, 0()) -> first()
     , greater(0(), s(y)) -> second()
     , greater(s(x), s(y)) -> greater(x, y)
     , double(0()) -> 0()
     , double(s(x)) -> s(s(double(x)))
     , triple(x) -> if(le(x, x, double(x)), x, 0(), 0())
     , if(false(), x, y, z) -> true()
     , if(first(), x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z))
     , if(second(), x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z) }
   Weak DPs:
     { le^#(s(x), 0(), z) -> c_2()
     , le^#(s(x), s(y), 0()) -> c_3()
     , greater^#(x, 0()) -> c_5()
     , greater^#(0(), s(y)) -> c_6()
     , double^#(0()) -> c_8()
     , if^#(false(), x, y, z) -> c_11() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..