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

#### Computed strongly connected components 
0. recursive  : [f3/5]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f12/3]
3. non_recursive  : [f3_loop_cont/4]
4. non_recursive  : [f0/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f3/5
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f3_loop_cont/4
4. SCC is partially evaluated into f0/3

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

### Specialization of cost equations f3/5 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 
* CE 3 is refined into CE [11] 
* CE 4 is refined into CE [12] 
* CE 2 is refined into CE [13] 


### Cost equations --> "Loop" of f3/5 
* CEs [11] --> Loop 9 
* CEs [12] --> Loop 10 
* CEs [13] --> Loop 11 
* CEs [9] --> Loop 12 
* CEs [10] --> Loop 13 

### Ranking functions of CR f3(A,B,D,E,F) 
* RF of phase [10]: [-A+10]

#### Partial ranking functions of CR f3(A,B,D,E,F) 
* Partial RF of phase [9,11]:
  - RF of loop [9:1]:
    -A+5 depends on loops [11:1] 
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    -A+10


### Specialization of cost equations f3_loop_cont/4 
* CE 8 is refined into CE [14] 
* CE 7 is refined into CE [15] 


### Cost equations --> "Loop" of f3_loop_cont/4 
* CEs [14] --> Loop 14 
* CEs [15] --> Loop 15 

### Ranking functions of CR f3_loop_cont(A,B,C,D) 

#### Partial ranking functions of CR f3_loop_cont(A,B,C,D) 


### Specialization of cost equations f0/3 
* CE 1 is refined into CE [16,17,18,19,20,21] 


### Cost equations --> "Loop" of f0/3 
* CEs [20,21] --> Loop 16 
* CEs [16,17,18,19] --> Loop 17 

### Ranking functions of CR f0(A,B,D) 

#### Partial ranking functions of CR f0(A,B,D) 


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

#### Cost of chains of f3(A,B,D,E,F):
* Chain [[9,11]]...: 2*it(9)+0
  with precondition: [5>=A] 

* Chain [[9,11],[10],13]: 2*it(9)+1*it(10)+0
  Such that:it(10) =< 4

  with precondition: [D=2,E=10,F=9,5>=A] 

* Chain [[9,11],[10],12]: 2*it(9)+1*it(10)+0
  Such that:it(10) =< 4

  with precondition: [D=3,5>=A] 

* Chain [[9,11],13]: 2*it(9)+0
  with precondition: [D=2,5>=A,E>=10] 

* Chain [[9,11],12]: 2*it(9)+0
  with precondition: [D=3,5>=A] 

* Chain [12]: 0
  with precondition: [D=3] 


#### Cost of chains of f3_loop_cont(A,B,C,D):
* Chain [15]: 0
  with precondition: [A=2] 

* Chain [14]: 0
  with precondition: [A=3] 


#### Cost of chains of f0(A,B,D):
* Chain [17]: 1*aux(2)+0
  with precondition: [] 

* Chain [16]...: 1*aux(3)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,D): 
-------------------------------------
* Chain [17] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [16]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,D): inf 
Asymptotic class: infinity 
* Total analysis performed in 49 ms.

