MAYBE

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

Strict Trs:
  { check(0()) -> zero()
  , check(s(0())) -> odd()
  , check(s(s(0()))) -> even()
  , check(s(s(s(x)))) -> check(s(x))
  , half(0()) -> 0()
  , half(s(0())) -> 0()
  , half(s(s(x))) -> s(half(x))
  , plus(0(), y) -> y
  , plus(s(x), y) -> s(plus(x, y))
  , times(x, y) -> timesIter(x, y, 0())
  , timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
  , if(zero(), x, y, z, u) -> z
  , if(odd(), x, y, z, u) -> timesIter(p(x), y, u)
  , if(even(), x, y, z, u) ->
    plus(timesIter(half(x), y, half(z)),
         timesIter(half(x), y, half(s(z))))
  , p(0()) -> 0()
  , p(s(x)) -> x }
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) '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 minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   
   3) '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) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { check^#(0()) -> c_1()
     , check^#(s(0())) -> c_2()
     , check^#(s(s(0()))) -> c_3()
     , check^#(s(s(s(x)))) -> c_4(check^#(s(x)))
     , half^#(0()) -> c_5()
     , half^#(s(0())) -> c_6()
     , half^#(s(s(x))) -> c_7(half^#(x))
     , plus^#(0(), y) -> c_8(y)
     , plus^#(s(x), y) -> c_9(plus^#(x, y))
     , times^#(x, y) -> c_10(timesIter^#(x, y, 0()))
     , timesIter^#(x, y, z) -> c_11(if^#(check(x), x, y, z, plus(z, y)))
     , if^#(zero(), x, y, z, u) -> c_12(z)
     , if^#(odd(), x, y, z, u) -> c_13(timesIter^#(p(x), y, u))
     , if^#(even(), x, y, z, u) ->
       c_14(plus^#(timesIter(half(x), y, half(z)),
                   timesIter(half(x), y, half(s(z)))))
     , p^#(0()) -> c_15()
     , p^#(s(x)) -> c_16(x) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { check^#(0()) -> c_1()
     , check^#(s(0())) -> c_2()
     , check^#(s(s(0()))) -> c_3()
     , check^#(s(s(s(x)))) -> c_4(check^#(s(x)))
     , half^#(0()) -> c_5()
     , half^#(s(0())) -> c_6()
     , half^#(s(s(x))) -> c_7(half^#(x))
     , plus^#(0(), y) -> c_8(y)
     , plus^#(s(x), y) -> c_9(plus^#(x, y))
     , times^#(x, y) -> c_10(timesIter^#(x, y, 0()))
     , timesIter^#(x, y, z) -> c_11(if^#(check(x), x, y, z, plus(z, y)))
     , if^#(zero(), x, y, z, u) -> c_12(z)
     , if^#(odd(), x, y, z, u) -> c_13(timesIter^#(p(x), y, u))
     , if^#(even(), x, y, z, u) ->
       c_14(plus^#(timesIter(half(x), y, half(z)),
                   timesIter(half(x), y, half(s(z)))))
     , p^#(0()) -> c_15()
     , p^#(s(x)) -> c_16(x) }
   Strict Trs:
     { check(0()) -> zero()
     , check(s(0())) -> odd()
     , check(s(s(0()))) -> even()
     , check(s(s(s(x)))) -> check(s(x))
     , half(0()) -> 0()
     , half(s(0())) -> 0()
     , half(s(s(x))) -> s(half(x))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
     , if(zero(), x, y, z, u) -> z
     , if(odd(), x, y, z, u) -> timesIter(p(x), y, u)
     , if(even(), x, y, z, u) ->
       plus(timesIter(half(x), y, half(z)),
            timesIter(half(x), y, half(s(z))))
     , p(0()) -> 0()
     , p(s(x)) -> x }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,3,5,6,15} by
   applications of Pre({1,2,3,5,6,15}) = {4,7,8,12,16}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: check^#(0()) -> c_1()
       , 2: check^#(s(0())) -> c_2()
       , 3: check^#(s(s(0()))) -> c_3()
       , 4: check^#(s(s(s(x)))) -> c_4(check^#(s(x)))
       , 5: half^#(0()) -> c_5()
       , 6: half^#(s(0())) -> c_6()
       , 7: half^#(s(s(x))) -> c_7(half^#(x))
       , 8: plus^#(0(), y) -> c_8(y)
       , 9: plus^#(s(x), y) -> c_9(plus^#(x, y))
       , 10: times^#(x, y) -> c_10(timesIter^#(x, y, 0()))
       , 11: timesIter^#(x, y, z) ->
             c_11(if^#(check(x), x, y, z, plus(z, y)))
       , 12: if^#(zero(), x, y, z, u) -> c_12(z)
       , 13: if^#(odd(), x, y, z, u) -> c_13(timesIter^#(p(x), y, u))
       , 14: if^#(even(), x, y, z, u) ->
             c_14(plus^#(timesIter(half(x), y, half(z)),
                         timesIter(half(x), y, half(s(z)))))
       , 15: p^#(0()) -> c_15()
       , 16: p^#(s(x)) -> c_16(x) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { check^#(s(s(s(x)))) -> c_4(check^#(s(x)))
     , half^#(s(s(x))) -> c_7(half^#(x))
     , plus^#(0(), y) -> c_8(y)
     , plus^#(s(x), y) -> c_9(plus^#(x, y))
     , times^#(x, y) -> c_10(timesIter^#(x, y, 0()))
     , timesIter^#(x, y, z) -> c_11(if^#(check(x), x, y, z, plus(z, y)))
     , if^#(zero(), x, y, z, u) -> c_12(z)
     , if^#(odd(), x, y, z, u) -> c_13(timesIter^#(p(x), y, u))
     , if^#(even(), x, y, z, u) ->
       c_14(plus^#(timesIter(half(x), y, half(z)),
                   timesIter(half(x), y, half(s(z)))))
     , p^#(s(x)) -> c_16(x) }
   Strict Trs:
     { check(0()) -> zero()
     , check(s(0())) -> odd()
     , check(s(s(0()))) -> even()
     , check(s(s(s(x)))) -> check(s(x))
     , half(0()) -> 0()
     , half(s(0())) -> 0()
     , half(s(s(x))) -> s(half(x))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y))
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) -> if(check(x), x, y, z, plus(z, y))
     , if(zero(), x, y, z, u) -> z
     , if(odd(), x, y, z, u) -> timesIter(p(x), y, u)
     , if(even(), x, y, z, u) ->
       plus(timesIter(half(x), y, half(z)),
            timesIter(half(x), y, half(s(z))))
     , p(0()) -> 0()
     , p(s(x)) -> x }
   Weak DPs:
     { check^#(0()) -> c_1()
     , check^#(s(0())) -> c_2()
     , check^#(s(s(0()))) -> c_3()
     , half^#(0()) -> c_5()
     , half^#(s(0())) -> c_6()
     , p^#(0()) -> c_15() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..