MAYBE

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

Strict Trs:
  { min(x, 0()) -> 0()
  , min(0(), y) -> 0()
  , min(s(x), s(y)) -> s(min(x, y))
  , max(x, 0()) -> x
  , max(0(), y) -> y
  , max(s(x), s(y)) -> s(max(x, y))
  , twice(0()) -> 0()
  , twice(s(x)) -> s(s(twice(x)))
  , -(x, 0()) -> x
  , -(s(x), s(y)) -> -(x, y)
  , p(s(x)) -> x
  , f(s(x), s(y)) ->
    f(-(max(s(x), s(y)), min(s(x), s(y))), p(twice(min(x, y)))) }
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) '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
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { min^#(x, 0()) -> c_1()
     , min^#(0(), y) -> c_2()
     , min^#(s(x), s(y)) -> c_3(min^#(x, y))
     , max^#(x, 0()) -> c_4(x)
     , max^#(0(), y) -> c_5(y)
     , max^#(s(x), s(y)) -> c_6(max^#(x, y))
     , twice^#(0()) -> c_7()
     , twice^#(s(x)) -> c_8(twice^#(x))
     , -^#(x, 0()) -> c_9(x)
     , -^#(s(x), s(y)) -> c_10(-^#(x, y))
     , p^#(s(x)) -> c_11(x)
     , f^#(s(x), s(y)) ->
       c_12(f^#(-(max(s(x), s(y)), min(s(x), s(y))),
                p(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:
     { min^#(x, 0()) -> c_1()
     , min^#(0(), y) -> c_2()
     , min^#(s(x), s(y)) -> c_3(min^#(x, y))
     , max^#(x, 0()) -> c_4(x)
     , max^#(0(), y) -> c_5(y)
     , max^#(s(x), s(y)) -> c_6(max^#(x, y))
     , twice^#(0()) -> c_7()
     , twice^#(s(x)) -> c_8(twice^#(x))
     , -^#(x, 0()) -> c_9(x)
     , -^#(s(x), s(y)) -> c_10(-^#(x, y))
     , p^#(s(x)) -> c_11(x)
     , f^#(s(x), s(y)) ->
       c_12(f^#(-(max(s(x), s(y)), min(s(x), s(y))),
                p(twice(min(x, y))))) }
   Strict Trs:
     { min(x, 0()) -> 0()
     , min(0(), y) -> 0()
     , min(s(x), s(y)) -> s(min(x, y))
     , max(x, 0()) -> x
     , max(0(), y) -> y
     , max(s(x), s(y)) -> s(max(x, y))
     , twice(0()) -> 0()
     , twice(s(x)) -> s(s(twice(x)))
     , -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)
     , p(s(x)) -> x
     , f(s(x), s(y)) ->
       f(-(max(s(x), s(y)), min(s(x), s(y))), p(twice(min(x, y)))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,7} by applications of
   Pre({1,2,7}) = {3,4,5,8,9,11}. Here rules are labeled as follows:
   
     DPs:
       { 1: min^#(x, 0()) -> c_1()
       , 2: min^#(0(), y) -> c_2()
       , 3: min^#(s(x), s(y)) -> c_3(min^#(x, y))
       , 4: max^#(x, 0()) -> c_4(x)
       , 5: max^#(0(), y) -> c_5(y)
       , 6: max^#(s(x), s(y)) -> c_6(max^#(x, y))
       , 7: twice^#(0()) -> c_7()
       , 8: twice^#(s(x)) -> c_8(twice^#(x))
       , 9: -^#(x, 0()) -> c_9(x)
       , 10: -^#(s(x), s(y)) -> c_10(-^#(x, y))
       , 11: p^#(s(x)) -> c_11(x)
       , 12: f^#(s(x), s(y)) ->
             c_12(f^#(-(max(s(x), s(y)), min(s(x), s(y))),
                      p(twice(min(x, y))))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { min^#(s(x), s(y)) -> c_3(min^#(x, y))
     , max^#(x, 0()) -> c_4(x)
     , max^#(0(), y) -> c_5(y)
     , max^#(s(x), s(y)) -> c_6(max^#(x, y))
     , twice^#(s(x)) -> c_8(twice^#(x))
     , -^#(x, 0()) -> c_9(x)
     , -^#(s(x), s(y)) -> c_10(-^#(x, y))
     , p^#(s(x)) -> c_11(x)
     , f^#(s(x), s(y)) ->
       c_12(f^#(-(max(s(x), s(y)), min(s(x), s(y))),
                p(twice(min(x, y))))) }
   Strict Trs:
     { min(x, 0()) -> 0()
     , min(0(), y) -> 0()
     , min(s(x), s(y)) -> s(min(x, y))
     , max(x, 0()) -> x
     , max(0(), y) -> y
     , max(s(x), s(y)) -> s(max(x, y))
     , twice(0()) -> 0()
     , twice(s(x)) -> s(s(twice(x)))
     , -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)
     , p(s(x)) -> x
     , f(s(x), s(y)) ->
       f(-(max(s(x), s(y)), min(s(x), s(y))), p(twice(min(x, y)))) }
   Weak DPs:
     { min^#(x, 0()) -> c_1()
     , min^#(0(), y) -> c_2()
     , twice^#(0()) -> c_7() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..