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

#### Computed strongly connected components 
0. recursive  : [f4/5]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f11/3]
3. non_recursive  : [f4_loop_cont/4]
4. non_recursive  : [f0/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f4/5
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f4_loop_cont/4
4. SCC is partially evaluated into f0/3

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

### Specialization of cost equations f4/5 
* CE 5 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 2 is refined into CE [10] 
* CE 3 is refined into CE [11] 


### Cost equations --> "Loop" of f4/5 
* CEs [10] --> Loop 8 
* CEs [11] --> Loop 9 
* CEs [8] --> Loop 10 
* CEs [9] --> Loop 11 

### Ranking functions of CR f4(A,B,F,G,H) 

#### Partial ranking functions of CR f4(A,B,F,G,H) 


### Specialization of cost equations f4_loop_cont/4 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 


### Cost equations --> "Loop" of f4_loop_cont/4 
* CEs [12] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR f4_loop_cont(A,B,C,D) 

#### Partial ranking functions of CR f4_loop_cont(A,B,C,D) 


### Specialization of cost equations f0/3 
* CE 1 is refined into CE [14,15,16,17,18] 


### Cost equations --> "Loop" of f0/3 
* CEs [17,18] --> Loop 14 
* CEs [14,15,16] --> Loop 15 

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

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


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

#### Cost of chains of f4(A,B,F,G,H):
* Chain [[8,9]]...: 2*it(8)+0
  with precondition: [B>=A+1] 

* Chain [[8,9],11]: 2*it(8)+0
  with precondition: [F=2,B>=A+1,G>=H] 

* Chain [[8,9],10]: 2*it(8)+0
  with precondition: [F=3,B>=A+1] 

* Chain [10]: 0
  with precondition: [F=3] 


#### Cost of chains of f4_loop_cont(A,B,C,D):
* Chain [13]: 0
  with precondition: [A=2] 

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


#### Cost of chains of f0(A,B,F):
* Chain [15]: 1*aux(1)+0
  with precondition: [] 

* Chain [14]...: 1*aux(2)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,F): 
-------------------------------------
* Chain [15] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [14]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,F): inf 
Asymptotic class: infinity 
* Total analysis performed in 28 ms.

