MAYBE

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

Strict Trs:
  { f(0()) -> true()
  , f(1()) -> false()
  , f(s(x)) -> f(x)
  , if(true(), s(x), s(y)) -> s(x)
  , if(false(), s(x), s(y)) -> s(y)
  , g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y)))
  , g(x, c(y)) -> c(g(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:
     { f^#(0()) -> c_1()
     , f^#(1()) -> c_2()
     , f^#(s(x)) -> c_3(f^#(x))
     , if^#(true(), s(x), s(y)) -> c_4(x)
     , if^#(false(), s(x), s(y)) -> c_5(y)
     , g^#(x, c(y)) -> c_6(g^#(x, if(f(x), c(g(s(x), y)), c(y))))
     , g^#(x, c(y)) -> c_7(g^#(x, y)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { f^#(0()) -> c_1()
     , f^#(1()) -> c_2()
     , f^#(s(x)) -> c_3(f^#(x))
     , if^#(true(), s(x), s(y)) -> c_4(x)
     , if^#(false(), s(x), s(y)) -> c_5(y)
     , g^#(x, c(y)) -> c_6(g^#(x, if(f(x), c(g(s(x), y)), c(y))))
     , g^#(x, c(y)) -> c_7(g^#(x, y)) }
   Strict Trs:
     { f(0()) -> true()
     , f(1()) -> false()
     , f(s(x)) -> f(x)
     , if(true(), s(x), s(y)) -> s(x)
     , if(false(), s(x), s(y)) -> s(y)
     , g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y)))
     , g(x, c(y)) -> c(g(x, y)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,6} by applications of
   Pre({1,2,6}) = {3,4,5,7}. Here rules are labeled as follows:
   
     DPs:
       { 1: f^#(0()) -> c_1()
       , 2: f^#(1()) -> c_2()
       , 3: f^#(s(x)) -> c_3(f^#(x))
       , 4: if^#(true(), s(x), s(y)) -> c_4(x)
       , 5: if^#(false(), s(x), s(y)) -> c_5(y)
       , 6: g^#(x, c(y)) -> c_6(g^#(x, if(f(x), c(g(s(x), y)), c(y))))
       , 7: g^#(x, c(y)) -> c_7(g^#(x, y)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { f^#(s(x)) -> c_3(f^#(x))
     , if^#(true(), s(x), s(y)) -> c_4(x)
     , if^#(false(), s(x), s(y)) -> c_5(y)
     , g^#(x, c(y)) -> c_7(g^#(x, y)) }
   Strict Trs:
     { f(0()) -> true()
     , f(1()) -> false()
     , f(s(x)) -> f(x)
     , if(true(), s(x), s(y)) -> s(x)
     , if(false(), s(x), s(y)) -> s(y)
     , g(x, c(y)) -> g(x, if(f(x), c(g(s(x), y)), c(y)))
     , g(x, c(y)) -> c(g(x, y)) }
   Weak DPs:
     { f^#(0()) -> c_1()
     , f^#(1()) -> c_2()
     , g^#(x, c(y)) -> c_6(g^#(x, if(f(x), c(g(s(x), y)), c(y)))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..