```* Step 1: MI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y)))
b(y,z) -> z
f(c(a(),z,x)) -> b(a(),z)
- Signature:
{b/2,f/1} / {a/0,c/3}
- Obligation:
runtime complexity wrt. defined symbols {b,f} and constructors {a,c}
+ Applied Processor:
MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity (Just 1))), miDimension = 2, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
+ Details:
We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity (Just 1))):

Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(a) = 

p(b) = [2 1] x_1 + [1 1] x_2 + 
[3 0]       [2 2]       
p(c) = [1 0] x_1 + [1 1] x_2 + [1 0] x_3 + 
[0 0]       [0 0]       [0 0]       
p(f) = [1 0] x_1 + 
[2 0]       

Following rules are strictly oriented:
b(x,b(z,y)) = [2 1] x + [3 3] y + [ 5 1] z + 
[3 0]     [6 6]     [10 2]     
> [1 0] x + [1 0] y + [ 5 1] z + 
[2 0]     [2 0]     [10 2]     
= f(b(f(f(z)),c(x,z,y)))

f(c(a(),z,x)) = [1 0] x + [1 1] z + 
[2 0]     [2 2]     
> [1 1] z + 
[2 2]     
= b(a(),z)

Following rules are (at-least) weakly oriented:
b(y,z) =  [2 1] y + [1 1] z + 
[3 0]     [2 2]     
>= [1 0] z + 
[0 1]     
=  z

* Step 2: MI WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
b(y,z) -> z
- Weak TRS:
b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y)))
f(c(a(),z,x)) -> b(a(),z)
- Signature:
{b/2,f/1} / {a/0,c/3}
- Obligation:
runtime complexity wrt. defined symbols {b,f} and constructors {a,c}
+ Applied Processor:
MI {miKind = MaximalMatrix (UpperTriangular (Multiplicity (Just 1))), miDimension = 2, miUArgs = UArgs, miURules = URules, miSelector = Just any strict-rules}
+ Details:
We apply a matrix interpretation of kind MaximalMatrix (UpperTriangular (Multiplicity (Just 1))):

Following symbols are considered usable:
all
TcT has computed the following interpretation:
p(a) = 

p(b) = [2 1] x_1 + [1 1] x_2 + 
[7 0]       [2 1]       
p(c) = [1 0] x_1 + [1 1] x_2 + [1 0] x_3 + 
[0 0]       [0 0]       [0 0]       
p(f) = [1 0] x_1 + 
[2 0]       

Following rules are strictly oriented:
b(y,z) = [2 1] y + [1 1] z + 
[7 0]     [2 1]     
> [1 0] z + 
[0 1]     
= z

Following rules are (at-least) weakly oriented:
b(x,b(z,y)) =  [2 1] x + [3 2] y + [ 9 1] z + 
[7 0]     [4 3]     [11 2]     
>= [1 0] x + [1 0] y + [ 5 1] z + 
[2 0]     [2 0]     [10 2]     
=  f(b(f(f(z)),c(x,z,y)))

f(c(a(),z,x)) =  [1 0] x + [1 1] z + 
[2 0]     [2 2]     
>= [1 1] z + 
[2 1]     
=  b(a(),z)

* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y)))
b(y,z) -> z
f(c(a(),z,x)) -> b(a(),z)
- Signature:
{b/2,f/1} / {a/0,c/3}
- Obligation:
runtime complexity wrt. defined symbols {b,f} and constructors {a,c}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

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