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

#### Computed strongly connected components 
0. recursive  : [f10/5,f14/5]
1. recursive  : [f10_loop_cont/10,f8/9]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f28/7]
4. non_recursive  : [f8_loop_cont/8]
5. non_recursive  : [f0/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f10/5
1. SCC is partially evaluated into f8/9
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f8_loop_cont/8
5. SCC is partially evaluated into f0/7

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

### Specialization of cost equations f10/5 
* CE 13 is refined into CE [14] 
* CE 12 is refined into CE [15] 
* CE 10 is refined into CE [16] 
* CE 9 is refined into CE [17] 
* CE 8 is refined into CE [18] 
* CE 11 is refined into CE [19] 


### Cost equations --> "Loop" of f10/5 
* CEs [16] --> Loop 14 
* CEs [17] --> Loop 15 
* CEs [18] --> Loop 16 
* CEs [19] --> Loop 17 
* CEs [14] --> Loop 18 
* CEs [15] --> Loop 19 

### Ranking functions of CR f10(D,E,H,I,J) 

#### Partial ranking functions of CR f10(D,E,H,I,J) 
* Partial RF of phase [14,15,16,17]:
  - RF of loop [16:1]:
    D-E depends on loops [14:1,15:1,17:1] 
    -E/2+3 depends on loops [14:1,15:1,17:1] 


### Specialization of cost equations f8/9 
* CE 4 is refined into CE [20] 
* CE 2 is refined into CE [21,22,23] 
* CE 5 is refined into CE [24] 
* CE 3 is refined into CE [25,26,27] 


### Cost equations --> "Loop" of f8/9 
* CEs [27] --> Loop 20 
* CEs [26] --> Loop 21 
* CEs [25] --> Loop 22 
* CEs [20] --> Loop 23 
* CEs [22] --> Loop 24 
* CEs [21] --> Loop 25 
* CEs [24] --> Loop 26 
* CEs [23] --> Loop 27 

### Ranking functions of CR f8(C,D,E,F,H,I,J,K,L) 

#### Partial ranking functions of CR f8(C,D,E,F,H,I,J,K,L) 
* Partial RF of phase [20,21,22]:
  - RF of loop [21:1]:
    -D/3+10 depends on loops [20:1] 
  - RF of loop [22:1]:
    -D/2+15 depends on loops [20:1] 
    -D/12+E/12+1/12 depends on loops [20:1,21:1] 


### Specialization of cost equations f8_loop_cont/8 
* CE 6 is refined into CE [28] 
* CE 7 is refined into CE [29] 


### Cost equations --> "Loop" of f8_loop_cont/8 
* CEs [28] --> Loop 28 
* CEs [29] --> Loop 29 

### Ranking functions of CR f8_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR f8_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations f0/7 
* CE 1 is refined into CE [30,31,32,33,34,35,36] 


### Cost equations --> "Loop" of f0/7 
* CEs [34,35,36] --> Loop 30 
* CEs [30,31,32,33] --> Loop 31 

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

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


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

#### Cost of chains of f10(D,E,H,I,J):
* Chain [[14,15,16,17]]...: 4*it(14)+0
  with precondition: [D>=E+1,H>=2,3>=H] 

* Chain [[14,15,16,17],19]: 4*it(14)+0
  with precondition: [H=2,I>=D+3,D>=E+1,J+12>=I] 

* Chain [[14,15,16,17],18]: 4*it(14)+0
  with precondition: [H=3,D>=E+1] 

* Chain [19]: 0
  with precondition: [H=2,D+2=I,E=J+10,E>=D] 

* Chain [18]: 0
  with precondition: [H=3] 


#### Cost of chains of f8(C,D,E,F,H,I,J,K,L):
* Chain [[20,21,22]]...: 11*it(20)+0
  with precondition: [C=0,29>=D] 

* Chain [[20,21,22],27]...: 15*it(20)+0
  with precondition: [C=0,H=3,29>=D,173>=5*D+E] 

* Chain [[20,21,22],26]: 11*it(20)+0
  with precondition: [C=0,H=3,29>=D] 

* Chain [[20,21,22],25]: 11*it(20)+0
  with precondition: [C=0,H=3,29>=D] 

* Chain [[20,21,22],24]: 15*it(20)+0
  with precondition: [C=0,H=3,29>=D,173>=5*D+E] 

* Chain [[20,21,22],23]: 11*it(20)+0
  with precondition: [C=0,H=4,I=1,L=1,29>=D,J>=30] 

* Chain [26]: 0
  with precondition: [C=0,H=3] 

* Chain [25]: 0
  with precondition: [C=0,H=3,29>=D] 


#### Cost of chains of f8_loop_cont(A,B,C,D,E,F,G,H):
* Chain [29]: 0
  with precondition: [A=3,B=1,C=1] 

* Chain [28]: 0
  with precondition: [A=4,B=1,C=1] 


#### Cost of chains of f0(A,B,C,D,E,F,H):
* Chain [31]: 1*aux(5)+0
  with precondition: [] 

* Chain [30]...: 1*aux(6)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,H): 
-------------------------------------
* 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,D,E,F,H): inf 
Asymptotic class: infinity 
* Total analysis performed in 142 ms.

