WARNING: Excluded non-linear constraints:[I*I>=C+1]
WARNING: Excluded non-linear constraints:[C>=I*I]

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

#### Computed strongly connected components 
0. recursive  : [f6/8]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f16/5]
3. non_recursive  : [f6_loop_cont/6]
4. non_recursive  : [f0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f6/8
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f6_loop_cont/6
4. SCC is partially evaluated into f0/5

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

### Specialization of cost equations f6/8 
* CE 5 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10] 
* CE 2 is refined into CE [11] 


### Cost equations --> "Loop" of f6/8 
* CEs [10] --> Loop 8 
* CEs [11] --> Loop 9 
* CEs [8] --> Loop 10 
* CEs [9] --> Loop 11 

### Ranking functions of CR f6(A,B,C,D,F,G,H,I) 

#### Partial ranking functions of CR f6(A,B,C,D,F,G,H,I) 


### Specialization of cost equations f6_loop_cont/6 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 


### Cost equations --> "Loop" of f6_loop_cont/6 
* CEs [12] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR f6_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR f6_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations f0/5 
* CE 1 is refined into CE [14,15,16,17,18,19] 


### Cost equations --> "Loop" of f0/5 
* CEs [18,19] --> Loop 14 
* CEs [15,17] --> Loop 15 
* CEs [14] --> Loop 16 
* CEs [16] --> Loop 17 

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

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


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

#### Cost of chains of f6(A,B,C,D,F,G,H,I):
* Chain [[8,9]]...: 2*it(8)+0
  with precondition: [B>=A+2] 

* Chain [[8,9],11]: 2*it(8)+0
  with precondition: [F=2,B>=A+2,G+1>=H,I+1>=H,G+1>=I] 

* Chain [[8,9],10]: 2*it(8)+0
  with precondition: [F=3,B>=A+2] 

* Chain [11]: 0
  with precondition: [F=2,I=D,A=G,B=H,A+1>=B] 

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


#### Cost of chains of f6_loop_cont(A,B,C,D,E,F):
* Chain [13]: 0
  with precondition: [A=2] 

* Chain [12]: 0
  with precondition: [A=3] 


#### Cost of chains of f0(A,B,C,D,F):
* Chain [17]: 0
  with precondition: [] 

* Chain [16]: 0
  with precondition: [2>=C] 

* Chain [15]: 1*aux(1)+0
  with precondition: [C>=3] 

* Chain [14]...: 1*aux(2)+0
  with precondition: [C>=3] 


Closed-form bounds of f0(A,B,C,D,F): 
-------------------------------------
* Chain [17] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [2>=C] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [C>=3] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [14]... with precondition: [C>=3] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,F): inf 
Asymptotic class: infinity 
* Total analysis performed in 45 ms.

