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

#### Computed strongly connected components 
0. recursive  : [f8/6]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f6/4]
3. non_recursive  : [f8_loop_cont/5]
4. non_recursive  : [f0/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f8/6
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f8_loop_cont/5
4. SCC is partially evaluated into f0/4

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

### Specialization of cost equations f8/6 
* CE 5 is refined into CE [8] 
* CE 3 is discarded (unfeasible) 
* CE 4 is refined into CE [9] 
* CE 2 is refined into CE [10] 


### Cost equations --> "Loop" of f8/6 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR f8(A,B,C,D,E,F) 
* RF of phase [8]: [-A+19,-2*C+19]

#### Partial ranking functions of CR f8(A,B,C,D,E,F) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    -A+19
    -2*C+19


### Specialization of cost equations f8_loop_cont/5 
* CE 7 is refined into CE [11] 
* CE 6 is refined into CE [12] 


### Cost equations --> "Loop" of f8_loop_cont/5 
* CEs [11] --> Loop 11 
* CEs [12] --> Loop 12 

### Ranking functions of CR f8_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f8_loop_cont(A,B,C,D,E) 


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


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

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

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


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

#### Cost of chains of f8(A,B,C,D,E,F):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< -A+19

  with precondition: [B=10,D=2,E=20,F=10,2*C=A,9>=C,C>=0] 

* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< -2*C+19

  with precondition: [B=10,D=3,2*C=A,9>=C,C>=0] 

* Chain [9]: 0
  with precondition: [B=10,D=3,A=2*C,A>=0] 


#### Cost of chains of f8_loop_cont(A,B,C,D,E):
* Chain [12]: 0
  with precondition: [A=2,C=10] 

* Chain [11]: 0
  with precondition: [A=3,C=10] 


#### Cost of chains of f0(A,B,C,D):
* Chain [13]: 38
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D): 
-------------------------------------
* Chain [13] with precondition: [] 
    - Upper bound: 38 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D): 38 
Asymptotic class: constant 
* Total analysis performed in 38 ms.

