MAYBE

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

Strict Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , cons(X1, X2) -> n__cons(X1, X2)
  , 0() -> n__0()
  , U11(tt(), L) -> s(length(activate(L)))
  , s(X) -> n__s(X)
  , length(X) -> n__length(X)
  , length(cons(N, L)) ->
    U11(and(isNatList(activate(L)), n__isNat(N)), activate(L))
  , length(nil()) -> 0()
  , activate(X) -> X
  , activate(n__zeros()) -> zeros()
  , activate(n__0()) -> 0()
  , activate(n__length(X)) -> length(activate(X))
  , activate(n__s(X)) -> s(activate(X))
  , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
  , activate(n__isNatIList(X)) -> isNatIList(X)
  , activate(n__nil()) -> nil()
  , activate(n__isNatList(X)) -> isNatList(X)
  , activate(n__isNat(X)) -> isNat(X)
  , and(tt(), X) -> activate(X)
  , isNat(X) -> n__isNat(X)
  , isNat(n__0()) -> tt()
  , isNat(n__length(V1)) -> isNatList(activate(V1))
  , isNat(n__s(V1)) -> isNat(activate(V1))
  , isNatList(X) -> n__isNatList(X)
  , isNatList(n__cons(V1, V2)) ->
    and(isNat(activate(V1)), n__isNatList(activate(V2)))
  , isNatList(n__nil()) -> tt()
  , isNatIList(V) -> isNatList(activate(V))
  , isNatIList(X) -> n__isNatIList(X)
  , isNatIList(n__zeros()) -> tt()
  , isNatIList(n__cons(V1, V2)) ->
    and(isNat(activate(V1)), n__isNatIList(activate(V2)))
  , nil() -> n__nil() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Arguments of following rules are not normal-forms:

{ length(cons(N, L)) ->
  U11(and(isNatList(activate(L)), n__isNat(N)), activate(L))
, length(nil()) -> 0() }

All above mentioned rules can be savely removed.

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

Strict Trs:
  { zeros() -> cons(0(), n__zeros())
  , zeros() -> n__zeros()
  , cons(X1, X2) -> n__cons(X1, X2)
  , 0() -> n__0()
  , U11(tt(), L) -> s(length(activate(L)))
  , s(X) -> n__s(X)
  , length(X) -> n__length(X)
  , activate(X) -> X
  , activate(n__zeros()) -> zeros()
  , activate(n__0()) -> 0()
  , activate(n__length(X)) -> length(activate(X))
  , activate(n__s(X)) -> s(activate(X))
  , activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
  , activate(n__isNatIList(X)) -> isNatIList(X)
  , activate(n__nil()) -> nil()
  , activate(n__isNatList(X)) -> isNatList(X)
  , activate(n__isNat(X)) -> isNat(X)
  , and(tt(), X) -> activate(X)
  , isNat(X) -> n__isNat(X)
  , isNat(n__0()) -> tt()
  , isNat(n__length(V1)) -> isNatList(activate(V1))
  , isNat(n__s(V1)) -> isNat(activate(V1))
  , isNatList(X) -> n__isNatList(X)
  , isNatList(n__cons(V1, V2)) ->
    and(isNat(activate(V1)), n__isNatList(activate(V2)))
  , isNatList(n__nil()) -> tt()
  , isNatIList(V) -> isNatList(activate(V))
  , isNatIList(X) -> n__isNatIList(X)
  , isNatIList(n__zeros()) -> tt()
  , isNatIList(n__cons(V1, V2)) ->
    and(isNat(activate(V1)), n__isNatIList(activate(V2)))
  , nil() -> n__nil() }
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..