```* 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) = [2] x_1 + [3]
p(activate) = [8] x_1 + [10]
p(cons) = [1] x_1 + [8] x_2 + [4]
p(from) = [1] x_1 + [4]
p(n__cons) = [1] x_1 + [1] x_2 + [0]
p(n__from) = [1] x_1 + [0]
p(s) = [0]

Following rules are strictly oriented:
2nd(cons(X,n__cons(Y,Z))) = [2] X + [16] Y + [16] Z + [11]
> [8] Y + [10]
= activate(Y)

activate(X) = [8] X + [10]
> [1] X + [0]
= X

activate(n__cons(X1,X2)) = [8] X1 + [8] X2 + [10]
> [1] X1 + [8] X2 + [4]
= cons(X1,X2)

activate(n__from(X)) = [8] X + [10]
> [1] X + [4]
= from(X)

cons(X1,X2) = [1] X1 + [8] X2 + [4]
> [1] X1 + [1] X2 + [0]
= n__cons(X1,X2)

from(X) = [1] X + [4]
> [1] X + [0]
= n__from(X)

Following rules are (at-least) weakly oriented:
from(X) =  [1] X + [4]
>= [1] X + [4]
=  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) = [9] x1 + [7]
p(activate) = [8] x1 + [1]
p(cons) = [4] x1 + [2] x2 + [1]
p(from) = [8] x1 + [15]
p(n__cons) = [1] x1 + [1] x2 + [0]
p(n__from) = [1] x1 + [2]
p(s) = [0]

Following rules are strictly oriented:
from(X) = [8] X + [15]
> [4] X + [5]
= cons(X,n__from(s(X)))

Following rules are (at-least) weakly oriented:
2nd(cons(X,n__cons(Y,Z))) =  [36] X + [18] Y + [18] Z + [16]
>= [8] Y + [1]
=  activate(Y)

activate(X) =  [8] X + [1]
>= [1] X + [0]
=  X

activate(n__cons(X1,X2)) =  [8] X1 + [8] X2 + [1]
>= [4] X1 + [2] X2 + [1]
=  cons(X1,X2)

activate(n__from(X)) =  [8] X + [17]
>= [8] X + [15]
=  from(X)

cons(X1,X2) =  [4] X1 + [2] X2 + [1]
>= [1] X1 + [1] X2 + [0]
=  n__cons(X1,X2)

from(X) =  [8] X + [15]
>= [1] X + [2]
=  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))
```