MAYBE

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

Strict Trs:
  { and(true(), X) -> activate(X)
  , and(false(), Y) -> false()
  , activate(X) -> X
  , activate(n__add(X1, X2)) -> add(activate(X1), X2)
  , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
  , activate(n__from(X)) -> from(X)
  , activate(n__s(X)) -> s(X)
  , if(true(), X, Y) -> activate(X)
  , if(false(), X, Y) -> activate(Y)
  , add(X1, X2) -> n__add(X1, X2)
  , add(0(), X) -> activate(X)
  , add(s(X), Y) -> s(n__add(activate(X), activate(Y)))
  , s(X) -> n__s(X)
  , first(X1, X2) -> n__first(X1, X2)
  , first(0(), X) -> nil()
  , first(s(X), cons(Y, Z)) ->
    cons(activate(Y), n__first(activate(X), activate(Z)))
  , from(X) -> cons(activate(X), n__from(n__s(activate(X))))
  , from(X) -> n__from(X) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Arguments of following rules are not normal-forms:

{ add(s(X), Y) -> s(n__add(activate(X), activate(Y)))
, first(s(X), cons(Y, Z)) ->
  cons(activate(Y), n__first(activate(X), activate(Z))) }

All above mentioned rules can be savely removed.

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

Strict Trs:
  { and(true(), X) -> activate(X)
  , and(false(), Y) -> false()
  , activate(X) -> X
  , activate(n__add(X1, X2)) -> add(activate(X1), X2)
  , activate(n__first(X1, X2)) -> first(activate(X1), activate(X2))
  , activate(n__from(X)) -> from(X)
  , activate(n__s(X)) -> s(X)
  , if(true(), X, Y) -> activate(X)
  , if(false(), X, Y) -> activate(Y)
  , add(X1, X2) -> n__add(X1, X2)
  , add(0(), X) -> activate(X)
  , s(X) -> n__s(X)
  , first(X1, X2) -> n__first(X1, X2)
  , first(0(), X) -> nil()
  , from(X) -> cons(activate(X), n__from(n__s(activate(X))))
  , from(X) -> n__from(X) }
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) '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 input cannot be shown compatible
         
         2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
            following reason:
            
            The input cannot be shown compatible
         
      
      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.
         
      
   


Arrrr..