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

#### Computed strongly connected components 
0. recursive  : [f6/7,f9/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f24/4]
3. non_recursive  : [f17/4]
4. non_recursive  : [f6_loop_cont/5]
5. non_recursive  : [f0/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f6/7
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f17/4
4. SCC is partially evaluated into f6_loop_cont/5
5. SCC is partially evaluated into f0/4

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

### Specialization of cost equations f6/7 
* CE 9 is refined into CE [15] 
* CE 6 is refined into CE [16] 
* CE 7 is refined into CE [17] 
* CE 8 is refined into CE [18] 
* CE 2 is refined into CE [19] 
* CE 4 is refined into CE [20] 
* CE 3 is refined into CE [21] 
* CE 5 is refined into CE [22] 


### Cost equations --> "Loop" of f6/7 
* CEs [19] --> Loop 15 
* CEs [20] --> Loop 16 
* CEs [21] --> Loop 17 
* CEs [22] --> Loop 18 
* CEs [15] --> Loop 19 
* CEs [16] --> Loop 20 
* CEs [17] --> Loop 21 
* CEs [18] --> Loop 22 

### Ranking functions of CR f6(A,B,C,E,F,G,H) 

#### Partial ranking functions of CR f6(A,B,C,E,F,G,H) 


### Specialization of cost equations f17/4 
* CE 13 is refined into CE [23] 
* CE 12 is refined into CE [24] 
* CE 14 is refined into CE [25] 


### Cost equations --> "Loop" of f17/4 
* CEs [23] --> Loop 23 
* CEs [24] --> Loop 24 
* CEs [25] --> Loop 25 

### Ranking functions of CR f17(A,B,C,E) 

#### Partial ranking functions of CR f17(A,B,C,E) 


### Specialization of cost equations f6_loop_cont/5 
* CE 11 is refined into CE [26] 
* CE 10 is refined into CE [27,28,29] 


### Cost equations --> "Loop" of f6_loop_cont/5 
* CEs [26] --> Loop 26 
* CEs [29] --> Loop 27 
* CEs [28] --> Loop 28 
* CEs [27] --> Loop 29 

### Ranking functions of CR f6_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f6_loop_cont(A,B,C,D,E) 


### Specialization of cost equations f0/4 
* CE 1 is refined into CE [30,31,32,33,34,35,36,37,38,39,40] 


### Cost equations --> "Loop" of f0/4 
* CEs [37,38,39,40] --> Loop 30 
* CEs [30,31,32,33,34,35,36] --> Loop 31 

### Ranking functions of CR f0(A,B,C,E) 

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


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

#### Cost of chains of f6(A,B,C,E,F,G,H):
* Chain [[15,16,17,18]]...: 4*it(15)+0
  with precondition: [C=0] 

* Chain [[15,16,17,18],22]: 4*it(15)+0
  with precondition: [C=0,E=2,F=0,H=0] 

* Chain [[15,16,17,18],21]: 4*it(15)+0
  with precondition: [C=0,E=2,G=0,H=1,0>=F+1] 

* Chain [[15,16,17,18],20]: 4*it(15)+0
  with precondition: [C=0,E=2,G=0,H=1,F>=1] 

* Chain [[15,16,17,18],19]: 4*it(15)+0
  with precondition: [C=0,E=3] 

* Chain [22]: 0
  with precondition: [A=0,C=0,E=2,F=0,H=0,G=B] 

* Chain [21]: 0
  with precondition: [C=0,E=2,G=0,H=1,A=F,0>=A+1] 

* Chain [20]: 0
  with precondition: [C=0,E=2,G=0,H=1,A=F,A>=1] 

* Chain [19]: 0
  with precondition: [C=0,E=3] 


#### Cost of chains of f17(A,B,C,E):
* Chain [25]: 0
  with precondition: [C=1] 

* Chain [24]: 0
  with precondition: [0>=C] 

* Chain [23]: 0
  with precondition: [C>=2] 


#### Cost of chains of f6_loop_cont(A,B,C,D,E):
* Chain [29]: 0
  with precondition: [A=2,D=1] 

* Chain [28]: 0
  with precondition: [A=2,0>=D] 

* Chain [27]: 0
  with precondition: [A=2,D>=2] 

* Chain [26]: 0
  with precondition: [A=3] 


#### Cost of chains of f0(A,B,C,E):
* Chain [31]: 1*aux(2)+0
  with precondition: [] 

* Chain [30]...: 1*aux(3)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,E): 
-------------------------------------
* Chain [31] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [30]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,E): inf 
Asymptotic class: infinity 
* Total analysis performed in 81 ms.

