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

#### Computed strongly connected components 
0. non_recursive  : [f5/4]
1. recursive  : [f7/5]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f7_loop_cont/5]
4. non_recursive  : [f0/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is completely evaluated into other SCCs
1. SCC is partially evaluated into f7/5
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f7_loop_cont/5
4. SCC is partially evaluated into f0/4

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

### Specialization of cost equations f7/5 
* CE 5 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10] 


### Cost equations --> "Loop" of f7/5 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR f7(B,C,E,F,G) 
* RF of phase [8]: [-B+36]

#### Partial ranking functions of CR f7(B,C,E,F,G) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    -B+36


### Specialization of cost equations f7_loop_cont/5 
* CE 7 is refined into CE [11] 
* CE 6 is refined into CE [12] 


### Cost equations --> "Loop" of f7_loop_cont/5 
* CEs [11] --> Loop 11 
* CEs [12] --> Loop 12 

### Ranking functions of CR f7_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f7_loop_cont(A,B,C,D,E) 


### Specialization of cost equations f0/4 
* CE 1 is refined into CE [13] 
* CE 2 is refined into CE [14,15,16] 


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

### 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 f7(B,C,E,F,G):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< -B+36

  with precondition: [E=2,F=36,B+G=C+36,35>=B,B>=0] 

* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< -B+36

  with precondition: [E=3,35>=B,B>=0] 

* Chain [9]: 0
  with precondition: [E=3,B>=0] 


#### Cost of chains of f7_loop_cont(A,B,C,D,E):
* Chain [12]: 0
  with precondition: [A=2,127>=B] 

* Chain [11]: 0
  with precondition: [A=3,127>=B] 


#### Cost of chains of f0(A,B,C,E):
* Chain [14]: 72
  with precondition: [127>=A] 

* Chain [13]: 0
  with precondition: [A>=128] 


Closed-form bounds of f0(A,B,C,E): 
-------------------------------------
* Chain [14] with precondition: [127>=A] 
    - Upper bound: 72 
    - Complexity: constant 
* Chain [13] with precondition: [A>=128] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,E): 72 
Asymptotic class: constant 
* Total analysis performed in 29 ms.

