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

#### Computed strongly connected components 
0. recursive  : [f7/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f21/6]
3. non_recursive  : [f7_loop_cont/7]
4. non_recursive  : [f0/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f7/7
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f7_loop_cont/7
4. SCC is partially evaluated into f0/6

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

### Specialization of cost equations f7/7 
* CE 8 is refined into CE [11] 
* CE 6 is refined into CE [12] 
* CE 7 is refined into CE [13] 
* CE 5 is refined into CE [14] 
* CE 4 is refined into CE [15] 


### Cost equations --> "Loop" of f7/7 
* CEs [15] --> Loop 9 
* CEs [11] --> Loop 10 
* CEs [12] --> Loop 11 
* CEs [13] --> Loop 12 
* CEs [14] --> Loop 13 

### Ranking functions of CR f7(B,C,D,E,G,H,I) 
* RF of phase [9]: [B-C+1,-C+1024]

#### Partial ranking functions of CR f7(B,C,D,E,G,H,I) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    B-C+1
    -C+1024


### Specialization of cost equations f7_loop_cont/7 
* CE 10 is refined into CE [16] 
* CE 9 is refined into CE [17] 


### Cost equations --> "Loop" of f7_loop_cont/7 
* CEs [16] --> Loop 14 
* CEs [17] --> Loop 15 

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

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


### Specialization of cost equations f0/6 
* CE 1 is refined into CE [18,19,20,21,22] 
* CE 2 is refined into CE [23,24,25,26,27] 
* CE 3 is refined into CE [28,29,30,31,32] 


### Cost equations --> "Loop" of f0/6 
* CEs [20,25,30] --> Loop 16 
* CEs [19,24,29] --> Loop 17 
* CEs [18,23,28] --> Loop 18 
* CEs [21,22,26,27,31,32] --> Loop 19 

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

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


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

#### Cost of chains of f7(B,C,D,E,G,H,I):
* Chain [[9],13]: 1*it(9)+0
  Such that:it(9) =< -D/2+I/2

  with precondition: [G=2,B+1=H,D+2*B+2=2*C+I,1023>=B,1022>=E,C>=0,E>=0,B>=C] 

* Chain [[9],12]: 1*it(9)+0
  Such that:it(9) =< -D/2+I/2

  with precondition: [G=2,B+1=H,D+2*B+2=2*C+I,1023>=B,0>=E+1,C>=0,B>=C] 

* Chain [[9],11]: 1*it(9)+0
  Such that:it(9) =< -D/2+I/2

  with precondition: [G=2,B+1=H,D+2*B+2=2*C+I,1023>=B,C>=0,E>=1023,B>=C] 

* Chain [[9],10]: 1*it(9)+0
  Such that:it(9) =< B-C+1

  with precondition: [G=3,1023>=B,C>=0,B>=C] 

* Chain [10]: 0
  with precondition: [G=3,1023>=B,B>=0,C>=0] 


#### Cost of chains of f7_loop_cont(A,B,C,D,E,F,G):
* Chain [15]: 0
  with precondition: [A=2,1023>=C,C>=0] 

* Chain [14]: 0
  with precondition: [A=3,1023>=C,C>=0] 


#### Cost of chains of f0(A,B,C,D,E,G):
* Chain [19]: 1026
  with precondition: [] 

* Chain [18]: 1026
  with precondition: [1022>=E,E>=0] 

* Chain [17]: 1026
  with precondition: [0>=E+1] 

* Chain [16]: 1026
  with precondition: [E>=1023] 


Closed-form bounds of f0(A,B,C,D,E,G): 
-------------------------------------
* Chain [19] with precondition: [] 
    - Upper bound: 1026 
    - Complexity: constant 
* Chain [18] with precondition: [1022>=E,E>=0] 
    - Upper bound: 1026 
    - Complexity: constant 
* Chain [17] with precondition: [0>=E+1] 
    - Upper bound: 1026 
    - Complexity: constant 
* Chain [16] with precondition: [E>=1023] 
    - Upper bound: 1026 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,G): 1026 
Asymptotic class: constant 
* Total analysis performed in 93 ms.

