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

#### Computed strongly connected components 
0. recursive  : [f2/4]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f2_loop_cont/2]
3. non_recursive  : [f300/5]
4. non_recursive  : [f1/5]

#### 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 completely evaluated into other SCCs
4. SCC is partially evaluated into f1/5

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

### Specialization of cost equations f2/4 
* CE 6 is refined into CE [7] 
* CE 5 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,F) 

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


### Specialization of cost equations f1/5 
* CE 3 is refined into CE [9] 
* CE 2 is refined into CE [10] 
* CE 1 is refined into CE [11] 
* CE 4 is refined into CE [12,13,14] 


### Cost equations --> "Loop" of f1/5 
* CEs [14] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [12,13] --> Loop 13 

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

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


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

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

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

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


#### Cost of chains of f1(A,B,C,D,F):
* Chain [13]: 1*aux(1)+0
  with precondition: [A=B,A=C] 

* Chain [12]: 0
  with precondition: [B>=A,C>=A+1,C>=B] 

* Chain [11]: 0
  with precondition: [B>=A,B>=C+1] 

* Chain [10]: 0
  with precondition: [A>=B+1] 

* Chain [9]...: 1*s(2)+0
  with precondition: [A=B,A=C] 


Closed-form bounds of f1(A,B,C,D,F): 
-------------------------------------
* Chain [13] with precondition: [A=B,A=C] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [12] with precondition: [B>=A,C>=A+1,C>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [11] with precondition: [B>=A,B>=C+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [10] with precondition: [A>=B+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [9]... with precondition: [A=B,A=C] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f1(A,B,C,D,F): inf 
Asymptotic class: infinity 
* Total analysis performed in 27 ms.

