MAYBE

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

Strict Trs:
  { le(0(), y) -> true()
  , le(s(x), 0()) -> false()
  , le(s(x), s(y)) -> le(x, y)
  , quot(x, 0()) -> quotZeroErro()
  , quot(x, s(y)) -> quotIter(x, s(y), 0(), 0(), 0())
  , quotIter(x, s(y), z, u, v) -> if(le(x, z), x, s(y), z, u, v)
  , if(true(), x, y, z, u, v) -> v
  , if(false(), x, y, z, u, v) ->
    if2(le(y, s(u)), x, y, s(z), s(u), v)
  , if2(true(), x, y, z, u, v) -> quotIter(x, y, z, 0(), s(v))
  , if2(false(), x, y, z, u, v) -> quotIter(x, y, z, u, v) }
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 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) '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) '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) -> c_1()
     , le^#(s(x), 0()) -> c_2()
     , le^#(s(x), s(y)) -> c_3(le^#(x, y))
     , quot^#(x, 0()) -> c_4()
     , quot^#(x, s(y)) -> c_5(quotIter^#(x, s(y), 0(), 0(), 0()))
     , quotIter^#(x, s(y), z, u, v) ->
       c_6(if^#(le(x, z), x, s(y), z, u, v))
     , if^#(true(), x, y, z, u, v) -> c_7(v)
     , if^#(false(), x, y, z, u, v) ->
       c_8(if2^#(le(y, s(u)), x, y, s(z), s(u), v))
     , if2^#(true(), x, y, z, u, v) ->
       c_9(quotIter^#(x, y, z, 0(), s(v)))
     , if2^#(false(), x, y, z, u, v) ->
       c_10(quotIter^#(x, y, z, u, v)) }
   
   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) -> c_1()
     , le^#(s(x), 0()) -> c_2()
     , le^#(s(x), s(y)) -> c_3(le^#(x, y))
     , quot^#(x, 0()) -> c_4()
     , quot^#(x, s(y)) -> c_5(quotIter^#(x, s(y), 0(), 0(), 0()))
     , quotIter^#(x, s(y), z, u, v) ->
       c_6(if^#(le(x, z), x, s(y), z, u, v))
     , if^#(true(), x, y, z, u, v) -> c_7(v)
     , if^#(false(), x, y, z, u, v) ->
       c_8(if2^#(le(y, s(u)), x, y, s(z), s(u), v))
     , if2^#(true(), x, y, z, u, v) ->
       c_9(quotIter^#(x, y, z, 0(), s(v)))
     , if2^#(false(), x, y, z, u, v) ->
       c_10(quotIter^#(x, y, z, u, v)) }
   Strict Trs:
     { le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , quot(x, 0()) -> quotZeroErro()
     , quot(x, s(y)) -> quotIter(x, s(y), 0(), 0(), 0())
     , quotIter(x, s(y), z, u, v) -> if(le(x, z), x, s(y), z, u, v)
     , if(true(), x, y, z, u, v) -> v
     , if(false(), x, y, z, u, v) ->
       if2(le(y, s(u)), x, y, s(z), s(u), v)
     , if2(true(), x, y, z, u, v) -> quotIter(x, y, z, 0(), s(v))
     , if2(false(), x, y, z, u, v) -> quotIter(x, y, z, u, v) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,4} by applications of
   Pre({1,2,4}) = {3,7}. Here rules are labeled as follows:
   
     DPs:
       { 1: le^#(0(), y) -> c_1()
       , 2: le^#(s(x), 0()) -> c_2()
       , 3: le^#(s(x), s(y)) -> c_3(le^#(x, y))
       , 4: quot^#(x, 0()) -> c_4()
       , 5: quot^#(x, s(y)) -> c_5(quotIter^#(x, s(y), 0(), 0(), 0()))
       , 6: quotIter^#(x, s(y), z, u, v) ->
            c_6(if^#(le(x, z), x, s(y), z, u, v))
       , 7: if^#(true(), x, y, z, u, v) -> c_7(v)
       , 8: if^#(false(), x, y, z, u, v) ->
            c_8(if2^#(le(y, s(u)), x, y, s(z), s(u), v))
       , 9: if2^#(true(), x, y, z, u, v) ->
            c_9(quotIter^#(x, y, z, 0(), s(v)))
       , 10: if2^#(false(), x, y, z, u, v) ->
             c_10(quotIter^#(x, y, z, u, v)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { le^#(s(x), s(y)) -> c_3(le^#(x, y))
     , quot^#(x, s(y)) -> c_5(quotIter^#(x, s(y), 0(), 0(), 0()))
     , quotIter^#(x, s(y), z, u, v) ->
       c_6(if^#(le(x, z), x, s(y), z, u, v))
     , if^#(true(), x, y, z, u, v) -> c_7(v)
     , if^#(false(), x, y, z, u, v) ->
       c_8(if2^#(le(y, s(u)), x, y, s(z), s(u), v))
     , if2^#(true(), x, y, z, u, v) ->
       c_9(quotIter^#(x, y, z, 0(), s(v)))
     , if2^#(false(), x, y, z, u, v) ->
       c_10(quotIter^#(x, y, z, u, v)) }
   Strict Trs:
     { le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , quot(x, 0()) -> quotZeroErro()
     , quot(x, s(y)) -> quotIter(x, s(y), 0(), 0(), 0())
     , quotIter(x, s(y), z, u, v) -> if(le(x, z), x, s(y), z, u, v)
     , if(true(), x, y, z, u, v) -> v
     , if(false(), x, y, z, u, v) ->
       if2(le(y, s(u)), x, y, s(z), s(u), v)
     , if2(true(), x, y, z, u, v) -> quotIter(x, y, z, 0(), s(v))
     , if2(false(), x, y, z, u, v) -> quotIter(x, y, z, u, v) }
   Weak DPs:
     { le^#(0(), y) -> c_1()
     , le^#(s(x), 0()) -> c_2()
     , quot^#(x, 0()) -> c_4() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..