```* Step 1: MI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(s(x),y,y) -> f(y,x,s(x))
g(x,y) -> x
g(x,y) -> y
- Signature:
{f/3,g/2} / {s/1}
- Obligation:
runtime complexity wrt. defined symbols {f,g} and constructors {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(f) = [5]
p(g) = [1] x_1 + [2] x_2 + [2]
p(s) = [0]

Following rules are strictly oriented:
g(x,y) = [1] x + [2] y + [2]
> [1] x + [0]
= x

g(x,y) = [1] x + [2] y + [2]
> [1] y + [0]
= y

Following rules are (at-least) weakly oriented:
f(s(x),y,y) =  [5]
>= [5]
=  f(y,x,s(x))

* Step 2: MI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(s(x),y,y) -> f(y,x,s(x))
- Weak TRS:
g(x,y) -> x
g(x,y) -> y
- Signature:
{f/3,g/2} / {s/1}
- Obligation:
runtime complexity wrt. defined symbols {f,g} and constructors {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(f) = [2] x_1 + [1] x_2 + [1] x_3 + [12]
p(g) = [2] x_1 + [2] x_2 + [1]
p(s) = [1] x_1 + [8]

Following rules are strictly oriented:
f(s(x),y,y) = [2] x + [2] y + [28]
> [2] x + [2] y + [20]
= f(y,x,s(x))

Following rules are (at-least) weakly oriented:
g(x,y) =  [2] x + [2] y + [1]
>= [1] x + [0]
=  x

g(x,y) =  [2] x + [2] y + [1]
>= [1] y + [0]
=  y

* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(s(x),y,y) -> f(y,x,s(x))
g(x,y) -> x
g(x,y) -> y
- Signature:
{f/3,g/2} / {s/1}
- Obligation:
runtime complexity wrt. defined symbols {f,g} and constructors {s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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