
Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [eval/3]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [eval_loop_cont/2]
3. non_recursive  : [start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval/3
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into start/3

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations eval/3 
* CE 3 is refined into CE [4] 
* CE 2 is refined into CE [5] 


### Cost equations --> "Loop" of eval/3 
* CEs [5] --> Loop 4 
* CEs [4] --> Loop 5 

### Ranking functions of CR eval(A,B,C) 

#### Partial ranking functions of CR eval(A,B,C) 


### Specialization of cost equations start/3 
* CE 1 is refined into CE [6,7] 


### Cost equations --> "Loop" of start/3 
* CEs [7] --> Loop 6 
* CEs [6] --> Loop 7 

### Ranking functions of CR start(A,B,C) 

#### Partial ranking functions of CR start(A,B,C) 


Computing Bounds
=====================================

#### Cost of chains of eval(A,B,C):
* Chain [5]: 0
  with precondition: [C=2] 

* Chain [4,5]: 1
  with precondition: [C=2,A>=B+1] 


#### Cost of chains of start(A,B,C):
* Chain [7]: 0
  with precondition: [] 

* Chain [6]: 1
  with precondition: [A>=B+1] 


Closed-form bounds of start(A,B,C): 
-------------------------------------
* Chain [7] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [6] with precondition: [A>=B+1] 
    - Upper bound: 1 
    - Complexity: constant 

### Maximum cost of start(A,B,C): 1 
Asymptotic class: constant 
* Total analysis performed in 9 ms.

