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

#### Computed strongly connected components 
0. recursive  : [f4/4]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f14/3]
3. non_recursive  : [f4_loop_cont/4]
4. non_recursive  : [f0/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f4/4
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/4
4. SCC is partially evaluated into f0/3

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

### Specialization of cost equations f4/4 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 
* CE 3 is refined into CE [11] 
* CE 4 is refined into CE [12] 
* CE 2 is refined into CE [13] 


### Cost equations --> "Loop" of f4/4 
* CEs [13] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR f4(A,B,D,E) 

#### Partial ranking functions of CR f4(A,B,D,E) 


### Specialization of cost equations f4_loop_cont/4 
* CE 8 is refined into CE [14] 
* CE 7 is refined into CE [15] 


### Cost equations --> "Loop" of f4_loop_cont/4 
* CEs [14] --> Loop 14 
* CEs [15] --> Loop 15 

### Ranking functions of CR f4_loop_cont(A,B,C,D) 

#### Partial ranking functions of CR f4_loop_cont(A,B,C,D) 


### Specialization of cost equations f0/3 
* CE 1 is refined into CE [16,17,18,19,20,21,22,23] 


### Cost equations --> "Loop" of f0/3 
* CEs [22,23] --> Loop 16 
* CEs [16,17,18,19,20,21] --> Loop 17 

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

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


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

#### Cost of chains of f4(A,B,D,E):
* Chain [[9]]...: 1*it(9)+0
  with precondition: [B>=0] 

* Chain [[9],13]: 1*it(9)+0
  with precondition: [D=2,0>=A+1,B>=0,E>=B+1] 

* Chain [[9],12]: 1*it(9)+0
  with precondition: [D=2,A>=0,B>=0,E>=A+1,E>=B+1] 

* Chain [[9],11]: 1*it(9)+0
  with precondition: [D=2,B>=0,E>=B+1,A>=E] 

* Chain [[9],10]: 1*it(9)+0
  with precondition: [D=3,B>=0] 

* Chain [13]: 0
  with precondition: [D=2,B=E,0>=A+1,B>=0] 

* Chain [11]: 0
  with precondition: [D=2,B=E,B>=0,A>=B] 

* Chain [10]: 0
  with precondition: [D=3,B>=0] 


#### Cost of chains of f4_loop_cont(A,B,C,D):
* Chain [15]: 0
  with precondition: [A=2] 

* Chain [14]: 0
  with precondition: [A=3] 


#### Cost of chains of f0(A,B,D):
* Chain [17]: 1*aux(2)+0
  with precondition: [] 

* Chain [16]...: 1*aux(3)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,D): 
-------------------------------------
* Chain [17] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [16]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,D): inf 
Asymptotic class: infinity 
* Total analysis performed in 37 ms.

