MAYBE

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

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


Arrrr..