MAYBE

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

Strict Trs:
  { plus(x, 0()) -> x
  , plus(x, s(y)) -> s(plus(x, y))
  , times(x, 0()) -> 0()
  , times(0(), y) -> 0()
  , times(s(x), y) -> plus(times(x, y), y)
  , p(s(0())) -> 0()
  , p(s(s(x))) -> s(p(s(x)))
  , fac(s(x)) -> times(fac(p(s(x))), s(x)) }
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) '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) '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
      
   

2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { plus^#(x, 0()) -> c_1(x)
     , plus^#(x, s(y)) -> c_2(plus^#(x, y))
     , times^#(x, 0()) -> c_3()
     , times^#(0(), y) -> c_4()
     , times^#(s(x), y) -> c_5(plus^#(times(x, y), y))
     , p^#(s(0())) -> c_6()
     , p^#(s(s(x))) -> c_7(p^#(s(x)))
     , fac^#(s(x)) -> c_8(times^#(fac(p(s(x))), s(x))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { plus^#(x, 0()) -> c_1(x)
     , plus^#(x, s(y)) -> c_2(plus^#(x, y))
     , times^#(x, 0()) -> c_3()
     , times^#(0(), y) -> c_4()
     , times^#(s(x), y) -> c_5(plus^#(times(x, y), y))
     , p^#(s(0())) -> c_6()
     , p^#(s(s(x))) -> c_7(p^#(s(x)))
     , fac^#(s(x)) -> c_8(times^#(fac(p(s(x))), s(x))) }
   Strict Trs:
     { plus(x, 0()) -> x
     , plus(x, s(y)) -> s(plus(x, y))
     , times(x, 0()) -> 0()
     , times(0(), y) -> 0()
     , times(s(x), y) -> plus(times(x, y), y)
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , fac(s(x)) -> times(fac(p(s(x))), s(x)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,4,6} by applications of
   Pre({3,4,6}) = {1,7,8}. Here rules are labeled as follows:
   
     DPs:
       { 1: plus^#(x, 0()) -> c_1(x)
       , 2: plus^#(x, s(y)) -> c_2(plus^#(x, y))
       , 3: times^#(x, 0()) -> c_3()
       , 4: times^#(0(), y) -> c_4()
       , 5: times^#(s(x), y) -> c_5(plus^#(times(x, y), y))
       , 6: p^#(s(0())) -> c_6()
       , 7: p^#(s(s(x))) -> c_7(p^#(s(x)))
       , 8: fac^#(s(x)) -> c_8(times^#(fac(p(s(x))), s(x))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { plus^#(x, 0()) -> c_1(x)
     , plus^#(x, s(y)) -> c_2(plus^#(x, y))
     , times^#(s(x), y) -> c_5(plus^#(times(x, y), y))
     , p^#(s(s(x))) -> c_7(p^#(s(x)))
     , fac^#(s(x)) -> c_8(times^#(fac(p(s(x))), s(x))) }
   Strict Trs:
     { plus(x, 0()) -> x
     , plus(x, s(y)) -> s(plus(x, y))
     , times(x, 0()) -> 0()
     , times(0(), y) -> 0()
     , times(s(x), y) -> plus(times(x, y), y)
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , fac(s(x)) -> times(fac(p(s(x))), s(x)) }
   Weak DPs:
     { times^#(x, 0()) -> c_3()
     , times^#(0(), y) -> c_4()
     , p^#(s(0())) -> c_6() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..