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

#### Computed strongly connected components 
0. recursive  : [f2/4]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f3/3]
3. non_recursive  : [f2_loop_cont/4]
4. non_recursive  : [f1/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/4
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f2_loop_cont/4
4. SCC is partially evaluated into f1/3

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

### Specialization of cost equations f2/4 
* CE 4 is refined into CE [7] 
* CE 3 is discarded (unfeasible) 
* CE 2 is refined into CE [8] 


### Cost equations --> "Loop" of f2/4 
* CEs [8] --> Loop 7 
* CEs [7] --> Loop 8 

### Ranking functions of CR f2(A,B,C,D) 

#### Partial ranking functions of CR f2(A,B,C,D) 


### Specialization of cost equations f2_loop_cont/4 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 


### Cost equations --> "Loop" of f2_loop_cont/4 
* CEs [9] --> Loop 9 
* CEs [10] --> Loop 10 

### Ranking functions of CR f2_loop_cont(A,B,C,D) 

#### Partial ranking functions of CR f2_loop_cont(A,B,C,D) 


### Specialization of cost equations f1/3 
* CE 1 is refined into CE [11,12,13] 


### Cost equations --> "Loop" of f1/3 
* CEs [12,13] --> Loop 11 
* CEs [11] --> Loop 12 

### Ranking functions of CR f1(A,B,C) 

#### Partial ranking functions of CR f1(A,B,C) 


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

#### Cost of chains of f2(A,B,C,D):
* Chain [[7]]...: 1*it(7)+0
  with precondition: [0>=B+2,A>=1] 

* Chain [[7],8]: 1*it(7)+0
  with precondition: [C=3,0>=B+2,A>=1] 

* Chain [8]: 0
  with precondition: [C=3,0>=B+2,A>=1] 


#### Cost of chains of f2_loop_cont(A,B,C,D):
* Chain [10]: 0
  with precondition: [A=2,0>=C+2] 

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


#### Cost of chains of f1(A,B,C):
* Chain [12]: 1*s(2)+0
  with precondition: [A>=1,0>=A+B+1] 

* Chain [11]...: 1*aux(2)+0
  with precondition: [A>=1,0>=A+B+1] 


Closed-form bounds of f1(A,B,C): 
-------------------------------------
* Chain [12] with precondition: [A>=1,0>=A+B+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [11]... with precondition: [A>=1,0>=A+B+1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f1(A,B,C): inf 
Asymptotic class: infinity 
* Total analysis performed in 23 ms.

