MAYBE

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

Strict Trs:
  { null(nil()) -> true()
  , null(add(n, x)) -> false()
  , tail(nil()) -> nil()
  , tail(add(n, x)) -> x
  , head(add(n, x)) -> n
  , app(nil(), y) -> y
  , app(add(n, x), y) -> add(n, app(x, y))
  , reverse(nil()) -> nil()
  , reverse(add(n, x)) -> app(reverse(x), add(n, nil()))
  , shuffle(x) -> shuff(x, nil())
  , shuff(x, y) -> if(null(x), x, y, app(y, add(head(x), nil())))
  , if(true(), x, y, z) -> y
  , if(false(), x, y, z) -> shuff(reverse(tail(x)), z) }
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:
     { null^#(nil()) -> c_1()
     , null^#(add(n, x)) -> c_2()
     , tail^#(nil()) -> c_3()
     , tail^#(add(n, x)) -> c_4(x)
     , head^#(add(n, x)) -> c_5(n)
     , app^#(nil(), y) -> c_6(y)
     , app^#(add(n, x), y) -> c_7(n, app^#(x, y))
     , reverse^#(nil()) -> c_8()
     , reverse^#(add(n, x)) -> c_9(app^#(reverse(x), add(n, nil())))
     , shuffle^#(x) -> c_10(shuff^#(x, nil()))
     , shuff^#(x, y) ->
       c_11(if^#(null(x), x, y, app(y, add(head(x), nil()))))
     , if^#(true(), x, y, z) -> c_12(y)
     , if^#(false(), x, y, z) -> c_13(shuff^#(reverse(tail(x)), z)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { null^#(nil()) -> c_1()
     , null^#(add(n, x)) -> c_2()
     , tail^#(nil()) -> c_3()
     , tail^#(add(n, x)) -> c_4(x)
     , head^#(add(n, x)) -> c_5(n)
     , app^#(nil(), y) -> c_6(y)
     , app^#(add(n, x), y) -> c_7(n, app^#(x, y))
     , reverse^#(nil()) -> c_8()
     , reverse^#(add(n, x)) -> c_9(app^#(reverse(x), add(n, nil())))
     , shuffle^#(x) -> c_10(shuff^#(x, nil()))
     , shuff^#(x, y) ->
       c_11(if^#(null(x), x, y, app(y, add(head(x), nil()))))
     , if^#(true(), x, y, z) -> c_12(y)
     , if^#(false(), x, y, z) -> c_13(shuff^#(reverse(tail(x)), z)) }
   Strict Trs:
     { null(nil()) -> true()
     , null(add(n, x)) -> false()
     , tail(nil()) -> nil()
     , tail(add(n, x)) -> x
     , head(add(n, x)) -> n
     , app(nil(), y) -> y
     , app(add(n, x), y) -> add(n, app(x, y))
     , reverse(nil()) -> nil()
     , reverse(add(n, x)) -> app(reverse(x), add(n, nil()))
     , shuffle(x) -> shuff(x, nil())
     , shuff(x, y) -> if(null(x), x, y, app(y, add(head(x), nil())))
     , if(true(), x, y, z) -> y
     , if(false(), x, y, z) -> shuff(reverse(tail(x)), z) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,3,8} by applications
   of Pre({1,2,3,8}) = {4,5,6,7,12}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: null^#(nil()) -> c_1()
       , 2: null^#(add(n, x)) -> c_2()
       , 3: tail^#(nil()) -> c_3()
       , 4: tail^#(add(n, x)) -> c_4(x)
       , 5: head^#(add(n, x)) -> c_5(n)
       , 6: app^#(nil(), y) -> c_6(y)
       , 7: app^#(add(n, x), y) -> c_7(n, app^#(x, y))
       , 8: reverse^#(nil()) -> c_8()
       , 9: reverse^#(add(n, x)) -> c_9(app^#(reverse(x), add(n, nil())))
       , 10: shuffle^#(x) -> c_10(shuff^#(x, nil()))
       , 11: shuff^#(x, y) ->
             c_11(if^#(null(x), x, y, app(y, add(head(x), nil()))))
       , 12: if^#(true(), x, y, z) -> c_12(y)
       , 13: if^#(false(), x, y, z) ->
             c_13(shuff^#(reverse(tail(x)), z)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { tail^#(add(n, x)) -> c_4(x)
     , head^#(add(n, x)) -> c_5(n)
     , app^#(nil(), y) -> c_6(y)
     , app^#(add(n, x), y) -> c_7(n, app^#(x, y))
     , reverse^#(add(n, x)) -> c_9(app^#(reverse(x), add(n, nil())))
     , shuffle^#(x) -> c_10(shuff^#(x, nil()))
     , shuff^#(x, y) ->
       c_11(if^#(null(x), x, y, app(y, add(head(x), nil()))))
     , if^#(true(), x, y, z) -> c_12(y)
     , if^#(false(), x, y, z) -> c_13(shuff^#(reverse(tail(x)), z)) }
   Strict Trs:
     { null(nil()) -> true()
     , null(add(n, x)) -> false()
     , tail(nil()) -> nil()
     , tail(add(n, x)) -> x
     , head(add(n, x)) -> n
     , app(nil(), y) -> y
     , app(add(n, x), y) -> add(n, app(x, y))
     , reverse(nil()) -> nil()
     , reverse(add(n, x)) -> app(reverse(x), add(n, nil()))
     , shuffle(x) -> shuff(x, nil())
     , shuff(x, y) -> if(null(x), x, y, app(y, add(head(x), nil())))
     , if(true(), x, y, z) -> y
     , if(false(), x, y, z) -> shuff(reverse(tail(x)), z) }
   Weak DPs:
     { null^#(nil()) -> c_1()
     , null^#(add(n, x)) -> c_2()
     , tail^#(nil()) -> c_3()
     , reverse^#(nil()) -> c_8() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..