MAYBE

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

Strict Trs:
  { app(l, nil()) -> l
  , app(nil(), k) -> k
  , app(cons(x, l), k) -> cons(x, app(l, k))
  , sum(app(l, cons(x, cons(y, k)))) ->
    sum(app(l, sum(cons(x, cons(y, k)))))
  , sum(cons(x, nil())) -> cons(x, nil())
  , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l))
  , plus(0(), y) -> y
  , plus(s(x), y) -> s(plus(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:
      
      Computation stopped due to timeout after 5.0 seconds.
   
   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:
     { app^#(l, nil()) -> c_1(l)
     , app^#(nil(), k) -> c_2(k)
     , app^#(cons(x, l), k) -> c_3(x, app^#(l, k))
     , sum^#(app(l, cons(x, cons(y, k)))) ->
       c_4(sum^#(app(l, sum(cons(x, cons(y, k))))))
     , sum^#(cons(x, nil())) -> c_5(x)
     , sum^#(cons(x, cons(y, l))) -> c_6(sum^#(cons(plus(x, y), l)))
     , plus^#(0(), y) -> c_7(y)
     , plus^#(s(x), y) -> c_8(plus^#(x, y)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { app^#(l, nil()) -> c_1(l)
     , app^#(nil(), k) -> c_2(k)
     , app^#(cons(x, l), k) -> c_3(x, app^#(l, k))
     , sum^#(app(l, cons(x, cons(y, k)))) ->
       c_4(sum^#(app(l, sum(cons(x, cons(y, k))))))
     , sum^#(cons(x, nil())) -> c_5(x)
     , sum^#(cons(x, cons(y, l))) -> c_6(sum^#(cons(plus(x, y), l)))
     , plus^#(0(), y) -> c_7(y)
     , plus^#(s(x), y) -> c_8(plus^#(x, y)) }
   Strict Trs:
     { app(l, nil()) -> l
     , app(nil(), k) -> k
     , app(cons(x, l), k) -> cons(x, app(l, k))
     , sum(app(l, cons(x, cons(y, k)))) ->
       sum(app(l, sum(cons(x, cons(y, k)))))
     , sum(cons(x, nil())) -> cons(x, nil())
     , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l))
     , plus(0(), y) -> y
     , plus(s(x), y) -> s(plus(x, y)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..