```* Step 1: MI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
activate(X) -> X
activate(n__cons(X1,X2)) -> cons(X1,X2)
activate(n__from(X)) -> from(X)
cons(X1,X2) -> n__cons(X1,X2)
from(X) -> cons(X,n__from(s(X)))
from(X) -> n__from(X)
- Signature:
{2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
- Obligation:
runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
+ Applied Processor:
MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity Nothing)), miDimension = 1, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
+ Details:
We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity Nothing)):

The following argument positions are considered usable:
none

Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(2nd) =  x_1 + 
p(activate) =  x_1 + 
p(cons) =  x_1 +  x_2 + 
p(from) =  x_1 + 
p(n__cons) =  x_1 +  x_2 + 
p(n__from) =  x_1 + 
p(s) = 

Following rules are strictly oriented:
2nd(cons(X,n__cons(Y,Z))) =  X +  Y +  Z + 
>  Y + 
= activate(Y)

activate(X) =  X + 
>  X + 
= X

activate(n__cons(X1,X2)) =  X1 +  X2 + 
>  X1 +  X2 + 
= cons(X1,X2)

activate(n__from(X)) =  X + 
>  X + 
= from(X)

cons(X1,X2) =  X1 +  X2 + 
>  X1 +  X2 + 
= n__cons(X1,X2)

from(X) =  X + 
>  X + 
= n__from(X)

Following rules are (at-least) weakly oriented:
from(X) =   X + 
>=  X + 
=  cons(X,n__from(s(X)))

* Step 2: WeightGap WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
from(X) -> cons(X,n__from(s(X)))
- Weak TRS:
2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
activate(X) -> X
activate(n__cons(X1,X2)) -> cons(X1,X2)
activate(n__from(X)) -> from(X)
cons(X1,X2) -> n__cons(X1,X2)
from(X) -> n__from(X)
- Signature:
{2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
- Obligation:
runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
+ Applied Processor:
WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
+ Details:
The weightgap principle applies using the following nonconstant growth matrix-interpretation:
We apply a matrix interpretation of kind constructor based matrix interpretation:
The following argument positions are considered usable:
none

Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(2nd) =  x1 + 
p(activate) =  x1 + 
p(cons) =  x1 +  x2 + 
p(from) =  x1 + 
p(n__cons) =  x1 +  x2 + 
p(n__from) =  x1 + 
p(s) = 

Following rules are strictly oriented:
from(X) =  X + 
>  X + 
= cons(X,n__from(s(X)))

Following rules are (at-least) weakly oriented:
2nd(cons(X,n__cons(Y,Z))) =   X +  Y +  Z + 
>=  Y + 
=  activate(Y)

activate(X) =   X + 
>=  X + 
=  X

activate(n__cons(X1,X2)) =   X1 +  X2 + 
>=  X1 +  X2 + 
=  cons(X1,X2)

activate(n__from(X)) =   X + 
>=  X + 
=  from(X)

cons(X1,X2) =   X1 +  X2 + 
>=  X1 +  X2 + 
=  n__cons(X1,X2)

from(X) =   X + 
>=  X + 
=  n__from(X)

Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
2nd(cons(X,n__cons(Y,Z))) -> activate(Y)
activate(X) -> X
activate(n__cons(X1,X2)) -> cons(X1,X2)
activate(n__from(X)) -> from(X)
cons(X1,X2) -> n__cons(X1,X2)
from(X) -> cons(X,n__from(s(X)))
from(X) -> n__from(X)
- Signature:
{2nd/1,activate/1,cons/2,from/1} / {n__cons/2,n__from/1,s/1}
- Obligation:
runtime complexity wrt. defined symbols {2nd,activate,cons,from} and constructors {n__cons,n__from,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))
```