MAYBE

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

Strict Trs:
  { quot(x, 0(), s(z)) -> s(quot(x, plus(z, s(0())), s(z)))
  , quot(0(), s(y), s(z)) -> 0()
  , quot(s(x), s(y), z) -> quot(x, y, z)
  , plus(0(), y) -> y
  , plus(s(x), y) -> s(plus(x, y)) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) '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.
      
   

2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { quot^#(x, 0(), s(z)) -> c_1(quot^#(x, plus(z, s(0())), s(z)))
     , quot^#(0(), s(y), s(z)) -> c_2()
     , quot^#(s(x), s(y), z) -> c_3(quot^#(x, y, z))
     , plus^#(0(), y) -> c_4(y)
     , plus^#(s(x), y) -> c_5(plus^#(x, y)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { quot^#(x, 0(), s(z)) -> c_1(quot^#(x, plus(z, s(0())), s(z)))
     , quot^#(0(), s(y), s(z)) -> c_2()
     , quot^#(s(x), s(y), z) -> c_3(quot^#(x, y, z))
     , plus^#(0(), y) -> c_4(y)
     , plus^#(s(x), y) -> c_5(plus^#(x, y)) }
   Strict Trs:
     { quot(x, 0(), s(z)) -> s(quot(x, plus(z, s(0())), s(z)))
     , quot(0(), s(y), s(z)) -> 0()
     , quot(s(x), s(y), z) -> quot(x, y, z)
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2} by applications of
   Pre({2}) = {1,3,4}. Here rules are labeled as follows:
   
     DPs:
       { 1: quot^#(x, 0(), s(z)) -> c_1(quot^#(x, plus(z, s(0())), s(z)))
       , 2: quot^#(0(), s(y), s(z)) -> c_2()
       , 3: quot^#(s(x), s(y), z) -> c_3(quot^#(x, y, z))
       , 4: plus^#(0(), y) -> c_4(y)
       , 5: plus^#(s(x), y) -> c_5(plus^#(x, y)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { quot^#(x, 0(), s(z)) -> c_1(quot^#(x, plus(z, s(0())), s(z)))
     , quot^#(s(x), s(y), z) -> c_3(quot^#(x, y, z))
     , plus^#(0(), y) -> c_4(y)
     , plus^#(s(x), y) -> c_5(plus^#(x, y)) }
   Strict Trs:
     { quot(x, 0(), s(z)) -> s(quot(x, plus(z, s(0())), s(z)))
     , quot(0(), s(y), s(z)) -> 0()
     , quot(s(x), s(y), z) -> quot(x, y, z)
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y)) }
   Weak DPs: { quot^#(0(), s(y), s(z)) -> c_2() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..