MAYBE

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

Strict Trs:
  { sel(X1, X2) -> n__sel(X1, X2)
  , sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
  , sel(0(), cons(X, Z)) -> X
  , s(X) -> n__s(X)
  , cons(X1, X2) -> n__cons(X1, X2)
  , activate(X) -> X
  , activate(n__first(X1, X2)) -> first(X1, X2)
  , activate(n__from(X)) -> from(X)
  , activate(n__0()) -> 0()
  , activate(n__cons(X1, X2)) -> cons(X1, X2)
  , activate(n__nil()) -> nil()
  , activate(n__s(X)) -> s(X)
  , activate(n__sel(X1, X2)) -> sel(X1, X2)
  , 0() -> n__0()
  , first(X1, X2) -> n__first(X1, X2)
  , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
  , first(0(), Z) -> nil()
  , nil() -> n__nil()
  , from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
  , sel1(0(), cons(X, Z)) -> quote(X)
  , quote(n__0()) -> 01()
  , quote(n__s(X)) -> s1(quote(activate(X)))
  , quote(n__sel(X, Z)) -> sel1(activate(X), activate(Z))
  , first1(s(X), cons(Y, Z)) ->
    cons1(quote(Y), first1(X, activate(Z)))
  , first1(0(), Z) -> nil1()
  , quote1(n__first(X, Z)) -> first1(activate(X), activate(Z))
  , quote1(n__cons(X, Z)) ->
    cons1(quote(activate(X)), quote1(activate(Z)))
  , quote1(n__nil()) -> nil1()
  , unquote(01()) -> 0()
  , unquote(s1(X)) -> s(unquote(X))
  , unquote1(nil1()) -> nil()
  , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
  , fcons(X, Z) -> cons(X, Z) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Arguments of following rules are not normal-forms:

{ sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
, sel(0(), cons(X, Z)) -> X
, first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
, first(0(), Z) -> nil()
, sel1(s(X), cons(Y, Z)) -> sel1(X, activate(Z))
, sel1(0(), cons(X, Z)) -> quote(X)
, first1(s(X), cons(Y, Z)) ->
  cons1(quote(Y), first1(X, activate(Z)))
, first1(0(), Z) -> nil1() }

All above mentioned rules can be savely removed.

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

Strict Trs:
  { sel(X1, X2) -> n__sel(X1, X2)
  , s(X) -> n__s(X)
  , cons(X1, X2) -> n__cons(X1, X2)
  , activate(X) -> X
  , activate(n__first(X1, X2)) -> first(X1, X2)
  , activate(n__from(X)) -> from(X)
  , activate(n__0()) -> 0()
  , activate(n__cons(X1, X2)) -> cons(X1, X2)
  , activate(n__nil()) -> nil()
  , activate(n__s(X)) -> s(X)
  , activate(n__sel(X1, X2)) -> sel(X1, X2)
  , 0() -> n__0()
  , first(X1, X2) -> n__first(X1, X2)
  , nil() -> n__nil()
  , from(X) -> cons(X, n__from(s(X)))
  , from(X) -> n__from(X)
  , quote(n__0()) -> 01()
  , quote(n__s(X)) -> s1(quote(activate(X)))
  , quote(n__sel(X, Z)) -> sel1(activate(X), activate(Z))
  , quote1(n__first(X, Z)) -> first1(activate(X), activate(Z))
  , quote1(n__cons(X, Z)) ->
    cons1(quote(activate(X)), quote1(activate(Z)))
  , quote1(n__nil()) -> nil1()
  , unquote(01()) -> 0()
  , unquote(s1(X)) -> s(unquote(X))
  , unquote1(nil1()) -> nil()
  , unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z))
  , fcons(X, Z) -> cons(X, Z) }
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 minimal-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
         2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
      
   


Arrrr..