MAYBE

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

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


Arrrr..