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

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

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/2
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f3/2

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

### Specialization of cost equations f2/2 
* CE 4 is refined into CE [5] 
* CE 2 is refined into CE [6] 
* CE 3 is refined into CE [7] 


### Cost equations --> "Loop" of f2/2 
* CEs [6] --> Loop 5 
* CEs [7] --> Loop 6 
* CEs [5] --> Loop 7 

### Ranking functions of CR f2(A,B) 
* RF of phase [5]: [A-1]

#### Partial ranking functions of CR f2(A,B) 
* Partial RF of phase [5]:
  - RF of loop [5:1]:
    A-1


### Specialization of cost equations f3/2 
* CE 1 is refined into CE [8,9,10,11,12] 


### Cost equations --> "Loop" of f3/2 
* CEs [11] --> Loop 8 
* CEs [12] --> Loop 9 
* CEs [10] --> Loop 10 
* CEs [9] --> Loop 11 
* CEs [8] --> Loop 12 

### Ranking functions of CR f3(A,B) 

#### Partial ranking functions of CR f3(A,B) 


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

#### Cost of chains of f2(A,B):
* Chain [[6]]...: 1*it(6)+0
  with precondition: [1>=A,B=2] 

* Chain [[6],7]: 1*it(6)+0
  with precondition: [B=2,1>=A] 

* Chain [[5],[6]]...: 1*it(5)+1*it(6)+0
  Such that:it(5) =< A

  with precondition: [B=2,A>=2] 

* Chain [[5],[6],7]: 1*it(5)+1*it(6)+0
  Such that:it(5) =< A

  with precondition: [B=2,A>=2] 

* Chain [[5],7]: 1*it(5)+0
  Such that:it(5) =< A

  with precondition: [B=2,A>=2] 

* Chain [7]: 0
  with precondition: [B=2] 


#### Cost of chains of f3(A,B):
* Chain [12]: 0
  with precondition: [] 

* Chain [11]: 1*s(4)+0
  with precondition: [1>=A] 

* Chain [10]: 2*s(6)+1*s(7)+0
  Such that:s(5) =< A
s(6) =< s(5)

  with precondition: [A>=2] 

* Chain [9]...: 1*s(8)+0
  with precondition: [1>=A] 

* Chain [8]...: 1*s(9)+1*s(10)+0
  Such that:s(9) =< A

  with precondition: [A>=2] 


Closed-form bounds of f3(A,B): 
-------------------------------------
* Chain [12] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [11] with precondition: [1>=A] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [10] with precondition: [A>=2] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [9]... with precondition: [1>=A] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [8]... with precondition: [A>=2] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f3(A,B): inf 
Asymptotic class: infinity 
* Total analysis performed in 26 ms.

