MAYBE

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

Strict Trs:
  { merge(x, nil()) -> x
  , merge(nil(), y) -> y
  , merge(.(x, y), .(u, v)) ->
    if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
  , if(true(), x, y) -> x
  , if(false(), x, y) -> x
  , ++(nil(), y) -> y
  , ++(.(x, y), z) -> .(x, ++(y, 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:
     { merge^#(x, nil()) -> c_1(x)
     , merge^#(nil(), y) -> c_2(y)
     , merge^#(.(x, y), .(u, v)) ->
       c_3(if^#(<(x, u),
                .(x, merge(y, .(u, v))),
                .(u, merge(.(x, y), v))))
     , if^#(true(), x, y) -> c_4(x)
     , if^#(false(), x, y) -> c_5(x)
     , ++^#(nil(), y) -> c_6(y)
     , ++^#(.(x, y), z) -> c_7(x, ++^#(y, z)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { merge^#(x, nil()) -> c_1(x)
     , merge^#(nil(), y) -> c_2(y)
     , merge^#(.(x, y), .(u, v)) ->
       c_3(if^#(<(x, u),
                .(x, merge(y, .(u, v))),
                .(u, merge(.(x, y), v))))
     , if^#(true(), x, y) -> c_4(x)
     , if^#(false(), x, y) -> c_5(x)
     , ++^#(nil(), y) -> c_6(y)
     , ++^#(.(x, y), z) -> c_7(x, ++^#(y, z)) }
   Strict Trs:
     { merge(x, nil()) -> x
     , merge(nil(), y) -> y
     , merge(.(x, y), .(u, v)) ->
       if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
     , if(true(), x, y) -> x
     , if(false(), x, y) -> x
     , ++(nil(), y) -> y
     , ++(.(x, y), z) -> .(x, ++(y, z)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3} by applications of
   Pre({3}) = {1,2,4,5,6,7}. Here rules are labeled as follows:
   
     DPs:
       { 1: merge^#(x, nil()) -> c_1(x)
       , 2: merge^#(nil(), y) -> c_2(y)
       , 3: merge^#(.(x, y), .(u, v)) ->
            c_3(if^#(<(x, u),
                     .(x, merge(y, .(u, v))),
                     .(u, merge(.(x, y), v))))
       , 4: if^#(true(), x, y) -> c_4(x)
       , 5: if^#(false(), x, y) -> c_5(x)
       , 6: ++^#(nil(), y) -> c_6(y)
       , 7: ++^#(.(x, y), z) -> c_7(x, ++^#(y, z)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { merge^#(x, nil()) -> c_1(x)
     , merge^#(nil(), y) -> c_2(y)
     , if^#(true(), x, y) -> c_4(x)
     , if^#(false(), x, y) -> c_5(x)
     , ++^#(nil(), y) -> c_6(y)
     , ++^#(.(x, y), z) -> c_7(x, ++^#(y, z)) }
   Strict Trs:
     { merge(x, nil()) -> x
     , merge(nil(), y) -> y
     , merge(.(x, y), .(u, v)) ->
       if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
     , if(true(), x, y) -> x
     , if(false(), x, y) -> x
     , ++(nil(), y) -> y
     , ++(.(x, y), z) -> .(x, ++(y, z)) }
   Weak DPs:
     { merge^#(.(x, y), .(u, v)) ->
       c_3(if^#(<(x, u),
                .(x, merge(y, .(u, v))),
                .(u, merge(.(x, y), v)))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..