MAYBE

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

Strict Trs:
  { and(tt(), T) -> T
  , isNatIList(IL) -> isNatList(activate(IL))
  , isNatIList(n__zeros()) -> tt()
  , isNatIList(n__cons(N, IL)) ->
    and(isNat(activate(N)), isNatIList(activate(IL)))
  , isNatList(n__cons(N, L)) ->
    and(isNat(activate(N)), isNatList(activate(L)))
  , isNatList(n__nil()) -> tt()
  , isNatList(n__take(N, IL)) ->
    and(isNat(activate(N)), isNatIList(activate(IL)))
  , activate(X) -> X
  , activate(n__0()) -> 0()
  , activate(n__s(X)) -> s(activate(X))
  , activate(n__length(X)) -> length(activate(X))
  , activate(n__zeros()) -> zeros()
  , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
  , activate(n__nil()) -> nil()
  , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
  , isNat(n__0()) -> tt()
  , isNat(n__s(N)) -> isNat(activate(N))
  , isNat(n__length(L)) -> isNatList(activate(L))
  , zeros() -> n__zeros()
  , zeros() -> cons(0(), n__zeros())
  , cons(X1, X2) -> n__cons(X1, X2)
  , 0() -> n__0()
  , take(X1, X2) -> n__take(X1, X2)
  , take(0(), IL) -> uTake1(isNatIList(IL))
  , take(s(M), cons(N, IL)) ->
    uTake2(and(isNat(M), and(isNat(N), isNatIList(activate(IL)))),
           M,
           N,
           activate(IL))
  , uTake1(tt()) -> nil()
  , nil() -> n__nil()
  , s(X) -> n__s(X)
  , uTake2(tt(), M, N, IL) ->
    cons(activate(N), n__take(activate(M), activate(IL)))
  , length(X) -> n__length(X)
  , length(cons(N, L)) ->
    uLength(and(isNat(N), isNatList(activate(L))), activate(L))
  , uLength(tt(), L) -> s(length(activate(L))) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Arguments of following rules are not normal-forms:

{ take(0(), IL) -> uTake1(isNatIList(IL))
, take(s(M), cons(N, IL)) ->
  uTake2(and(isNat(M), and(isNat(N), isNatIList(activate(IL)))),
         M,
         N,
         activate(IL))
, length(cons(N, L)) ->
  uLength(and(isNat(N), isNatList(activate(L))), activate(L)) }

All above mentioned rules can be savely removed.

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

Strict Trs:
  { and(tt(), T) -> T
  , isNatIList(IL) -> isNatList(activate(IL))
  , isNatIList(n__zeros()) -> tt()
  , isNatIList(n__cons(N, IL)) ->
    and(isNat(activate(N)), isNatIList(activate(IL)))
  , isNatList(n__cons(N, L)) ->
    and(isNat(activate(N)), isNatList(activate(L)))
  , isNatList(n__nil()) -> tt()
  , isNatList(n__take(N, IL)) ->
    and(isNat(activate(N)), isNatIList(activate(IL)))
  , activate(X) -> X
  , activate(n__0()) -> 0()
  , activate(n__s(X)) -> s(activate(X))
  , activate(n__length(X)) -> length(activate(X))
  , activate(n__zeros()) -> zeros()
  , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
  , activate(n__nil()) -> nil()
  , activate(n__take(X1, X2)) -> take(activate(X1), activate(X2))
  , isNat(n__0()) -> tt()
  , isNat(n__s(N)) -> isNat(activate(N))
  , isNat(n__length(L)) -> isNatList(activate(L))
  , zeros() -> n__zeros()
  , zeros() -> cons(0(), n__zeros())
  , cons(X1, X2) -> n__cons(X1, X2)
  , 0() -> n__0()
  , take(X1, X2) -> n__take(X1, X2)
  , uTake1(tt()) -> nil()
  , nil() -> n__nil()
  , s(X) -> n__s(X)
  , uTake2(tt(), M, N, IL) ->
    cons(activate(N), n__take(activate(M), activate(IL)))
  , length(X) -> n__length(X)
  , uLength(tt(), L) -> s(length(activate(L))) }
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..