MAYBE

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

Strict Trs:
  { a__nats() -> a__adx(a__zeros())
  , a__nats() -> nats()
  , a__adx(X) -> adx(X)
  , a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y)))
  , a__zeros() -> cons(0(), zeros())
  , a__zeros() -> zeros()
  , a__incr(X) -> incr(X)
  , a__incr(cons(X, Y)) -> cons(s(X), incr(Y))
  , a__hd(X) -> hd(X)
  , a__hd(cons(X, Y)) -> mark(X)
  , mark(cons(X1, X2)) -> cons(X1, X2)
  , mark(0()) -> 0()
  , mark(zeros()) -> a__zeros()
  , mark(s(X)) -> s(X)
  , mark(incr(X)) -> a__incr(mark(X))
  , mark(adx(X)) -> a__adx(mark(X))
  , mark(nats()) -> a__nats()
  , mark(hd(X)) -> a__hd(mark(X))
  , mark(tl(X)) -> a__tl(mark(X))
  , a__tl(X) -> tl(X)
  , a__tl(cons(X, Y)) -> mark(Y) }
Obligation:
  runtime complexity
Answer:
  MAYBE

The input is overlay and right-linear. Switching to innermost
rewriting.

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

Strict Trs:
  { a__nats() -> a__adx(a__zeros())
  , a__nats() -> nats()
  , a__adx(X) -> adx(X)
  , a__adx(cons(X, Y)) -> a__incr(cons(X, adx(Y)))
  , a__zeros() -> cons(0(), zeros())
  , a__zeros() -> zeros()
  , a__incr(X) -> incr(X)
  , a__incr(cons(X, Y)) -> cons(s(X), incr(Y))
  , a__hd(X) -> hd(X)
  , a__hd(cons(X, Y)) -> mark(X)
  , mark(cons(X1, X2)) -> cons(X1, X2)
  , mark(0()) -> 0()
  , mark(zeros()) -> a__zeros()
  , mark(s(X)) -> s(X)
  , mark(incr(X)) -> a__incr(mark(X))
  , mark(adx(X)) -> a__adx(mark(X))
  , mark(nats()) -> a__nats()
  , mark(hd(X)) -> a__hd(mark(X))
  , mark(tl(X)) -> a__tl(mark(X))
  , a__tl(X) -> tl(X)
  , a__tl(cons(X, Y)) -> mark(Y) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.

2) 'Best' failed due to the following reason:
   
   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) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
            following reason:
            
            The input cannot be shown compatible
         
         2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
            to the following reason:
            
            The input cannot be shown compatible
         
      
   


Arrrr..