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

#### Computed strongly connected components 
0. recursive  : [f4/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f5/4]
3. non_recursive  : [f4_loop_cont/5]
4. non_recursive  : [f0/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f4/7
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/5
4. SCC is partially evaluated into f0/4

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

### Specialization of cost equations f4/7 
* CE 4 is refined into CE [7] 
* CE 2 is discarded (unfeasible) 
* CE 3 is refined into CE [8] 


### Cost equations --> "Loop" of f4/7 
* CEs [8] --> Loop 7 
* CEs [7] --> Loop 8 

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

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


### Specialization of cost equations f4_loop_cont/5 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 


### Cost equations --> "Loop" of f4_loop_cont/5 
* CEs [9] --> Loop 9 
* CEs [10] --> Loop 10 

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

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


### Specialization of cost equations f0/4 
* CE 1 is refined into CE [11,12,13,14] 


### Cost equations --> "Loop" of f0/4 
* CEs [13,14] --> Loop 11 
* CEs [11,12] --> Loop 12 

### Ranking functions of CR f0(A,B,C,E) 

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


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

#### Cost of chains of f4(A,B,C,E,F,G,H):
* Chain [[7]]...: 1*it(7)+0
  with precondition: [A+1=B] 

* Chain [[7],8]: 1*it(7)+0
  with precondition: [E=3,A+1=B] 

* Chain [8]: 0
  with precondition: [E=3,B=A+1] 


#### Cost of chains of f4_loop_cont(A,B,C,D,E):
* Chain [10]: 0
  with precondition: [A=2] 

* Chain [9]: 0
  with precondition: [A=3] 


#### Cost of chains of f0(A,B,C,E):
* Chain [12]: 1*aux(1)+0
  with precondition: [] 

* Chain [11]...: 1*aux(2)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,E): 
-------------------------------------
* Chain [12] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [11]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,E): inf 
Asymptotic class: infinity 
* Total analysis performed in 24 ms.

