MAYBE

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

Strict Trs:
  { -(x, 0()) -> x
  , -(s(x), s(y)) -> -(x, y)
  , min(x, 0()) -> 0()
  , min(0(), y) -> 0()
  , min(s(x), s(y)) -> s(min(x, y))
  , twice(0()) -> 0()
  , twice(s(x)) -> s(s(twice(x)))
  , f(s(x), s(y)) -> f(-(x, min(x, y)), s(twice(min(x, y))))
  , f(s(x), s(y)) -> f(-(y, min(x, y)), s(twice(min(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 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.
      
   

2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { -^#(x, 0()) -> c_1(x)
     , -^#(s(x), s(y)) -> c_2(-^#(x, y))
     , min^#(x, 0()) -> c_3()
     , min^#(0(), y) -> c_4()
     , min^#(s(x), s(y)) -> c_5(min^#(x, y))
     , twice^#(0()) -> c_6()
     , twice^#(s(x)) -> c_7(twice^#(x))
     , f^#(s(x), s(y)) -> c_8(f^#(-(x, min(x, y)), s(twice(min(x, y)))))
     , f^#(s(x), s(y)) ->
       c_9(f^#(-(y, min(x, y)), s(twice(min(x, y))))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { -^#(x, 0()) -> c_1(x)
     , -^#(s(x), s(y)) -> c_2(-^#(x, y))
     , min^#(x, 0()) -> c_3()
     , min^#(0(), y) -> c_4()
     , min^#(s(x), s(y)) -> c_5(min^#(x, y))
     , twice^#(0()) -> c_6()
     , twice^#(s(x)) -> c_7(twice^#(x))
     , f^#(s(x), s(y)) -> c_8(f^#(-(x, min(x, y)), s(twice(min(x, y)))))
     , f^#(s(x), s(y)) ->
       c_9(f^#(-(y, min(x, y)), s(twice(min(x, y))))) }
   Strict Trs:
     { -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)
     , min(x, 0()) -> 0()
     , min(0(), y) -> 0()
     , min(s(x), s(y)) -> s(min(x, y))
     , twice(0()) -> 0()
     , twice(s(x)) -> s(s(twice(x)))
     , f(s(x), s(y)) -> f(-(x, min(x, y)), s(twice(min(x, y))))
     , f(s(x), s(y)) -> f(-(y, min(x, y)), s(twice(min(x, y)))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,4,6} by applications of
   Pre({3,4,6}) = {1,5,7}. Here rules are labeled as follows:
   
     DPs:
       { 1: -^#(x, 0()) -> c_1(x)
       , 2: -^#(s(x), s(y)) -> c_2(-^#(x, y))
       , 3: min^#(x, 0()) -> c_3()
       , 4: min^#(0(), y) -> c_4()
       , 5: min^#(s(x), s(y)) -> c_5(min^#(x, y))
       , 6: twice^#(0()) -> c_6()
       , 7: twice^#(s(x)) -> c_7(twice^#(x))
       , 8: f^#(s(x), s(y)) ->
            c_8(f^#(-(x, min(x, y)), s(twice(min(x, y)))))
       , 9: f^#(s(x), s(y)) ->
            c_9(f^#(-(y, min(x, y)), s(twice(min(x, y))))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { -^#(x, 0()) -> c_1(x)
     , -^#(s(x), s(y)) -> c_2(-^#(x, y))
     , min^#(s(x), s(y)) -> c_5(min^#(x, y))
     , twice^#(s(x)) -> c_7(twice^#(x))
     , f^#(s(x), s(y)) -> c_8(f^#(-(x, min(x, y)), s(twice(min(x, y)))))
     , f^#(s(x), s(y)) ->
       c_9(f^#(-(y, min(x, y)), s(twice(min(x, y))))) }
   Strict Trs:
     { -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)
     , min(x, 0()) -> 0()
     , min(0(), y) -> 0()
     , min(s(x), s(y)) -> s(min(x, y))
     , twice(0()) -> 0()
     , twice(s(x)) -> s(s(twice(x)))
     , f(s(x), s(y)) -> f(-(x, min(x, y)), s(twice(min(x, y))))
     , f(s(x), s(y)) -> f(-(y, min(x, y)), s(twice(min(x, y)))) }
   Weak DPs:
     { min^#(x, 0()) -> c_3()
     , min^#(0(), y) -> c_4()
     , twice^#(0()) -> c_6() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..