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

#### Computed strongly connected components 
0. recursive  : [f1/5]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f3/4]
3. non_recursive  : [f1_loop_cont/5]
4. non_recursive  : [f2/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/5
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f1_loop_cont/5
4. SCC is partially evaluated into f2/4

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

### Specialization of cost equations f1/5 
* CE 5 is refined into CE [8] 
* CE 3 is refined into CE [9] 
* CE 4 is refined into CE [10] 


### Cost equations --> "Loop" of f1/5 
* CEs [10] --> Loop 7 
* CEs [8] --> Loop 8 
* CEs [9] --> Loop 9 

### Ranking functions of CR f1(A,B,F,G,H) 
* RF of phase [7]: [-A+500]

#### Partial ranking functions of CR f1(A,B,F,G,H) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    -A+500


### Specialization of cost equations f1_loop_cont/5 
* CE 7 is refined into CE [11] 
* CE 6 is refined into CE [12] 


### Cost equations --> "Loop" of f1_loop_cont/5 
* CEs [11] --> Loop 10 
* CEs [12] --> Loop 11 

### Ranking functions of CR f1_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f1_loop_cont(A,B,C,D,E) 


### Specialization of cost equations f2/4 
* CE 1 is refined into CE [13] 
* CE 2 is refined into CE [14,15,16,17] 


### Cost equations --> "Loop" of f2/4 
* CEs [13,14,15,16,17] --> Loop 12 

### Ranking functions of CR f2(A,B,C,F) 

#### Partial ranking functions of CR f2(A,B,C,F) 


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

#### Cost of chains of f1(A,B,F,G,H):
* Chain [[7],9]: 1*it(7)+0
  Such that:it(7) =< -A+500

  with precondition: [F=2,G=500,499>=A] 

* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< -A+500

  with precondition: [F=3,499>=A] 

* Chain [9]: 0
  with precondition: [A=500,F=2,G=500] 

* Chain [8]: 0
  with precondition: [F=3,500>=A] 


#### Cost of chains of f1_loop_cont(A,B,C,D,E):
* Chain [11]: 0
  with precondition: [A=2,499>=D] 

* Chain [10]: 0
  with precondition: [A=3,499>=D] 


#### Cost of chains of f2(A,B,C,F):
* Chain [12]: 1*aux(1)+0
  with precondition: [] 


Closed-form bounds of f2(A,B,C,F): 
-------------------------------------
* Chain [12] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f2(A,B,C,F): inf 
Asymptotic class: infinity 
* Total analysis performed in 33 ms.

