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

#### Computed strongly connected components 
0. recursive  : [f4/11]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f9/7]
3. non_recursive  : [f4_loop_cont/8]
4. non_recursive  : [f10/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f4/11
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f4_loop_cont/8
4. SCC is partially evaluated into f10/7

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

### Specialization of cost equations f4/11 
* CE 4 is refined into CE [7] 
* CE 2 is refined into CE [8] 
* CE 3 is refined into CE [9] 


### Cost equations --> "Loop" of f4/11 
* CEs [9] --> Loop 7 
* CEs [7] --> Loop 8 
* CEs [8] --> Loop 9 

### Ranking functions of CR f4(B,C,D,E,F,I,J,K,L,M,N) 

#### Partial ranking functions of CR f4(B,C,D,E,F,I,J,K,L,M,N) 


### Specialization of cost equations f4_loop_cont/8 
* CE 6 is refined into CE [10] 
* CE 5 is refined into CE [11] 


### Cost equations --> "Loop" of f4_loop_cont/8 
* CEs [10] --> Loop 10 
* CEs [11] --> Loop 11 

### Ranking functions of CR f4_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR f4_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations f10/7 
* CE 1 is refined into CE [12,13,14,15,16] 


### Cost equations --> "Loop" of f10/7 
* CEs [15,16] --> Loop 12 
* CEs [12,13,14] --> Loop 13 

### Ranking functions of CR f10(A,B,C,D,E,F,I) 

#### Partial ranking functions of CR f10(A,B,C,D,E,F,I) 


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

#### Cost of chains of f4(B,C,D,E,F,I,J,K,L,M,N):
* Chain [[7]]...: 1*it(7)+0
  with precondition: [B>=0] 

* Chain [[7],9]: 1*it(7)+0
  with precondition: [I=2,K=L,K=M,K=N,B>=0,J>=B+1] 

* Chain [[7],8]: 1*it(7)+0
  with precondition: [I=3,B>=0] 

* Chain [9]: 0
  with precondition: [I=2,N=F,B=J,C=K,C=L,C=M,B>=0] 

* Chain [8]: 0
  with precondition: [I=3,B>=0] 


#### Cost of chains of f4_loop_cont(A,B,C,D,E,F,G,H):
* Chain [11]: 0
  with precondition: [A=2,B=4] 

* Chain [10]: 0
  with precondition: [A=3,B=4] 


#### Cost of chains of f10(A,B,C,D,E,F,I):
* Chain [13]: 1*aux(2)+0
  with precondition: [] 

* Chain [12]...: 1*aux(3)+0
  with precondition: [] 


Closed-form bounds of f10(A,B,C,D,E,F,I): 
-------------------------------------
* Chain [13] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [12]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f10(A,B,C,D,E,F,I): inf 
Asymptotic class: infinity 
* Total analysis performed in 44 ms.

