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

#### Computed strongly connected components 
0. recursive  : [f5/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f16/4]
3. non_recursive  : [f5_loop_cont/5]
4. non_recursive  : [f0/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f5/7
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f5_loop_cont/5
4. SCC is partially evaluated into f0/4

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

### Specialization of cost equations f5/7 
* CE 4 is refined into CE [7] 
* CE 3 is refined into CE [8] 
* CE 2 is refined into CE [9] 


### Cost equations --> "Loop" of f5/7 
* CEs [9] --> Loop 7 
* CEs [7] --> Loop 8 
* CEs [8] --> Loop 9 

### Ranking functions of CR f5(A,B,C,F,G,H,I) 

#### Partial ranking functions of CR f5(A,B,C,F,G,H,I) 


### Specialization of cost equations f5_loop_cont/5 
* CE 6 is refined into CE [10] 
* CE 5 is refined into CE [11] 


### Cost equations --> "Loop" of f5_loop_cont/5 
* CEs [10] --> Loop 10 
* CEs [11] --> Loop 11 

### Ranking functions of CR f5_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f5_loop_cont(A,B,C,D,E) 


### Specialization of cost equations f0/4 
* CE 1 is refined into CE [12,13,14,15,16,17] 


### Cost equations --> "Loop" of f0/4 
* CEs [16,17] --> Loop 12 
* CEs [12,13,14,15] --> Loop 13 

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

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


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

#### Cost of chains of f5(A,B,C,F,G,H,I):
* Chain [[7]]...: 1*it(7)+0
  with precondition: [B>=0,2*A=B] 

* Chain [[7],9]: 1*it(7)+0
  with precondition: [F=2,B=2*A,2*G=H,B>=0,2*G>=B+2] 

* Chain [[7],8]: 1*it(7)+0
  with precondition: [F=3,B=2*A,B>=0] 

* Chain [9]: 0
  with precondition: [F=2,2*A=B,I=C,A=G,2*A=H,A>=0] 

* Chain [8]: 0
  with precondition: [F=3,2*A=B,A>=0] 


#### Cost of chains of f5_loop_cont(A,B,C,D,E):
* Chain [11]: 0
  with precondition: [A=2] 

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


#### Cost of chains of f0(A,B,C,F):
* Chain [13]: 1*aux(1)+0
  with precondition: [] 

* Chain [12]...: 1*aux(2)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,F): 
-------------------------------------
* Chain [13] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [12]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,F): inf 
Asymptotic class: infinity 
* Total analysis performed in 35 ms.

