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

#### Computed strongly connected components 
0. recursive  : [f2/3]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f2_loop_cont/2]
3. non_recursive  : [f0/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/3
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f0/3

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

### Specialization of cost equations f2/3 
* CE 9 is refined into CE [10] 
* CE 3 is refined into CE [11] 
* CE 5 is discarded (unfeasible) 
* CE 6 is refined into CE [12] 
* CE 8 is discarded (unfeasible) 
* CE 7 is discarded (unfeasible) 
* CE 4 is refined into CE [13] 


### Cost equations --> "Loop" of f2/3 
* CEs [11] --> Loop 9 
* CEs [12] --> Loop 10 
* CEs [13] --> Loop 11 
* CEs [10] --> Loop 12 

### Ranking functions of CR f2(A,B,E) 

#### Partial ranking functions of CR f2(A,B,E) 
* Partial RF of phase [9,10,11]:
  - RF of loop [9:1]:
    A-9 depends on loops [10:1] 
  - RF of loop [11:1]:
    A-5 depends on loops [10:1] 


### Specialization of cost equations f0/3 
* CE 1 is refined into CE [14,15,16] 
* CE 2 is refined into CE [17,18,19] 


### Cost equations --> "Loop" of f0/3 
* CEs [16,19] --> Loop 13 
* CEs [14,15,17,18] --> Loop 14 

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

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


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

#### Cost of chains of f2(A,B,E):
* Chain [[9,10,11]]...: 3*it(9)+0
  with precondition: [2*A>=3*B+3,A>=2*B,2*B+1>=A,E=2] 

* Chain [[9,10,11],12]: 3*it(9)+0
  with precondition: [E=2,2*A>=3*B+3,A>=2*B,2*B+1>=A] 

* Chain [12]: 0
  with precondition: [E=2,A>=3] 


#### Cost of chains of f0(A,B,E):
* Chain [14]: 1*aux(24)+0
  with precondition: [] 

* Chain [13]...: 1*aux(25)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,E): 
-------------------------------------
* Chain [14] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [13]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,E): inf 
Asymptotic class: infinity 
* Total analysis performed in 60 ms.

