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

#### Computed strongly connected components 
0. recursive  : [f19/3]
1. recursive  : [f10/3,f19_loop_cont/4,f9/3]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f9_loop_cont/2]
4. non_recursive  : [f0/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f19/3
1. SCC is partially evaluated into f9/3
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f0/3

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

### Specialization of cost equations f19/3 
* CE 10 is refined into CE [11] 
* CE 9 is refined into CE [12] 
* CE 8 is refined into CE [13] 


### Cost equations --> "Loop" of f19/3 
* CEs [13] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR f19(A,D,E) 
* RF of phase [11]: [A-2]

#### Partial ranking functions of CR f19(A,D,E) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    A-2


### Specialization of cost equations f9/3 
* CE 5 is refined into CE [14,15] 
* CE 7 is refined into CE [16] 
* CE 3 is refined into CE [17] 
* CE 4 is refined into CE [18] 
* CE 2 is refined into CE [19] 
* CE 6 is refined into CE [20] 


### Cost equations --> "Loop" of f9/3 
* CEs [17] --> Loop 14 
* CEs [18] --> Loop 15 
* CEs [19] --> Loop 16 
* CEs [20] --> Loop 17 
* CEs [14,15] --> Loop 18 
* CEs [16] --> Loop 19 

### Ranking functions of CR f9(A,B,D) 

#### Partial ranking functions of CR f9(A,B,D) 
* Partial RF of phase [14,15,16,17]:
  - RF of loop [16:1]:
    -A+6 depends on loops [17:1] 
  - RF of loop [17:1]:
    A/2-5/2 depends on loops [14:1,15:1,16:1] 


### Specialization of cost equations f0/3 
* CE 1 is refined into CE [21,22,23] 


### Cost equations --> "Loop" of f0/3 
* CEs [23] --> Loop 20 
* CEs [21,22] --> Loop 21 

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

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


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

#### Cost of chains of f19(A,D,E):
* Chain [[11],13]: 1*it(11)+0
  Such that:it(11) =< A

  with precondition: [D=2,E=2,A>=3] 

* Chain [[11],12]: 1*it(11)+0
  Such that:it(11) =< A

  with precondition: [D=3,A>=3] 

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


#### Cost of chains of f9(A,B,D):
* Chain [[14,15,16,17]]...: 5*it(14)+0
  with precondition: [D=3] 

* Chain [[14,15,16,17],19]: 5*it(14)+0
  with precondition: [D=3] 

* Chain [[14,15,16,17],18]: 6*it(14)+0
  with precondition: [D=3] 

* Chain [19]: 0
  with precondition: [D=3] 

* Chain [18]: 1*s(4)+0
  Such that:s(4) =< A

  with precondition: [D=3,A>=6] 


#### Cost of chains of f0(A,B,D):
* Chain [21]: 1*aux(26)+0
  with precondition: [] 

* Chain [20]...: 5*s(10)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,D): 
-------------------------------------
* Chain [21] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [20]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,D): inf 
Asymptotic class: infinity 
* Total analysis performed in 64 ms.

