MAYBE

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

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


Arrrr..