MAYBE

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

Strict Trs:
  { fact(X) -> if(zero(X), s(0()), prod(X, fact(p(X))))
  , if(true(), X, Y) -> X
  , if(false(), X, Y) -> Y
  , zero(s(X)) -> false()
  , zero(0()) -> true()
  , prod(s(X), Y) -> add(Y, prod(X, Y))
  , prod(0(), X) -> 0()
  , p(s(X)) -> X
  , add(s(X), Y) -> s(add(X, Y))
  , add(0(), 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) '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:
     { fact^#(X) -> c_1(if^#(zero(X), s(0()), prod(X, fact(p(X)))))
     , if^#(true(), X, Y) -> c_2(X)
     , if^#(false(), X, Y) -> c_3(Y)
     , zero^#(s(X)) -> c_4()
     , zero^#(0()) -> c_5()
     , prod^#(s(X), Y) -> c_6(add^#(Y, prod(X, Y)))
     , prod^#(0(), X) -> c_7()
     , add^#(s(X), Y) -> c_9(add^#(X, Y))
     , add^#(0(), X) -> c_10(X)
     , p^#(s(X)) -> c_8(X) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { fact^#(X) -> c_1(if^#(zero(X), s(0()), prod(X, fact(p(X)))))
     , if^#(true(), X, Y) -> c_2(X)
     , if^#(false(), X, Y) -> c_3(Y)
     , zero^#(s(X)) -> c_4()
     , zero^#(0()) -> c_5()
     , prod^#(s(X), Y) -> c_6(add^#(Y, prod(X, Y)))
     , prod^#(0(), X) -> c_7()
     , add^#(s(X), Y) -> c_9(add^#(X, Y))
     , add^#(0(), X) -> c_10(X)
     , p^#(s(X)) -> c_8(X) }
   Strict Trs:
     { fact(X) -> if(zero(X), s(0()), prod(X, fact(p(X))))
     , if(true(), X, Y) -> X
     , if(false(), X, Y) -> Y
     , zero(s(X)) -> false()
     , zero(0()) -> true()
     , prod(s(X), Y) -> add(Y, prod(X, Y))
     , prod(0(), X) -> 0()
     , p(s(X)) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , add(0(), X) -> X }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {4,5,7} by applications of
   Pre({4,5,7}) = {2,3,9,10}. Here rules are labeled as follows:
   
     DPs:
       { 1: fact^#(X) -> c_1(if^#(zero(X), s(0()), prod(X, fact(p(X)))))
       , 2: if^#(true(), X, Y) -> c_2(X)
       , 3: if^#(false(), X, Y) -> c_3(Y)
       , 4: zero^#(s(X)) -> c_4()
       , 5: zero^#(0()) -> c_5()
       , 6: prod^#(s(X), Y) -> c_6(add^#(Y, prod(X, Y)))
       , 7: prod^#(0(), X) -> c_7()
       , 8: add^#(s(X), Y) -> c_9(add^#(X, Y))
       , 9: add^#(0(), X) -> c_10(X)
       , 10: p^#(s(X)) -> c_8(X) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { fact^#(X) -> c_1(if^#(zero(X), s(0()), prod(X, fact(p(X)))))
     , if^#(true(), X, Y) -> c_2(X)
     , if^#(false(), X, Y) -> c_3(Y)
     , prod^#(s(X), Y) -> c_6(add^#(Y, prod(X, Y)))
     , add^#(s(X), Y) -> c_9(add^#(X, Y))
     , add^#(0(), X) -> c_10(X)
     , p^#(s(X)) -> c_8(X) }
   Strict Trs:
     { fact(X) -> if(zero(X), s(0()), prod(X, fact(p(X))))
     , if(true(), X, Y) -> X
     , if(false(), X, Y) -> Y
     , zero(s(X)) -> false()
     , zero(0()) -> true()
     , prod(s(X), Y) -> add(Y, prod(X, Y))
     , prod(0(), X) -> 0()
     , p(s(X)) -> X
     , add(s(X), Y) -> s(add(X, Y))
     , add(0(), X) -> X }
   Weak DPs:
     { zero^#(s(X)) -> c_4()
     , zero^#(0()) -> c_5()
     , prod^#(0(), X) -> c_7() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..