```* 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) = 
p(g) =  x_1 +  x_2 + 
p(s) = 

Following rules are strictly oriented:
g(x,y) =  x +  y + 
>  x + 
= x

g(x,y) =  x +  y + 
>  y + 
= y

Following rules are (at-least) weakly oriented:
f(s(x),y,y) =  
>= 
=  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) =  x_1 +  x_2 +  x_3 + 
p(g) =  x_1 +  x_2 + 
p(s) =  x_1 + 

Following rules are strictly oriented:
f(s(x),y,y) =  x +  y + 
>  x +  y + 
= f(y,x,s(x))

Following rules are (at-least) weakly oriented:
g(x,y) =   x +  y + 
>=  x + 
=  x

g(x,y) =   x +  y + 
>=  y + 
=  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))
```