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

#### Computed strongly connected components 
0. recursive  : [f16/8]
1. recursive  : [f10/11,f16_loop_cont/12]
2. non_recursive  : [exit_location/1]
3. recursive  : [f25/1]
4. non_recursive  : [f25_loop_cont/2]
5. non_recursive  : [f10_loop_cont/7]
6. non_recursive  : [f0/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f16/8
1. SCC is partially evaluated into f10/11
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f25/1
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into f10_loop_cont/7
6. SCC is partially evaluated into f0/6

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

### Specialization of cost equations f16/8 
* CE 10 is refined into CE [13] 
* CE 9 is discarded (unfeasible) 
* CE 8 is refined into CE [14] 


### Cost equations --> "Loop" of f16/8 
* CEs [14] --> Loop 13 
* CEs [13] --> Loop 14 

### Ranking functions of CR f16(A,C,D,E,G,H,I,J) 

#### Partial ranking functions of CR f16(A,C,D,E,G,H,I,J) 


### Specialization of cost equations f10/11 
* CE 4 is refined into CE [15] 
* CE 2 is refined into CE [16,17] 
* CE 5 is refined into CE [18] 
* CE 3 is refined into CE [19] 


### Cost equations --> "Loop" of f10/11 
* CEs [19] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [18] --> Loop 18 
* CEs [17] --> Loop 19 

### Ranking functions of CR f10(A,B,C,D,E,G,H,I,J,K,L) 

#### Partial ranking functions of CR f10(A,B,C,D,E,G,H,I,J,K,L) 


### Specialization of cost equations f25/1 
* CE 12 is refined into CE [20] 
* CE 11 is refined into CE [21] 


### Cost equations --> "Loop" of f25/1 
* CEs [21] --> Loop 20 
* CEs [20] --> Loop 21 

### Ranking functions of CR f25(G) 

#### Partial ranking functions of CR f25(G) 


### Specialization of cost equations f10_loop_cont/7 
* CE 7 is refined into CE [22,23] 
* CE 6 is refined into CE [24] 


### Cost equations --> "Loop" of f10_loop_cont/7 
* CEs [22] --> Loop 22 
* CEs [24] --> Loop 23 
* CEs [23] --> Loop 24 

### Ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G) 


### Specialization of cost equations f0/6 
* CE 1 is refined into CE [25,26,27,28,29,30,31,32,33,34] 


### Cost equations --> "Loop" of f0/6 
* CEs [28,30,31,32,33,34] --> Loop 25 
* CEs [25,26,27,29] --> Loop 26 

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

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


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

#### Cost of chains of f16(A,C,D,E,G,H,I,J):
* Chain [[13]]...: 1*it(13)+0
  with precondition: [0>=A,C>=1,G>=2,3>=G] 

* Chain [[13],14]: 1*it(13)+0
  with precondition: [G=3,0>=A,C>=1] 

* Chain [14]: 0
  with precondition: [G=3,0>=A,C>=1] 


#### Cost of chains of f10(A,B,C,D,E,G,H,I,J,K,L):
* Chain [[15]]...: 2*it(15)+0
  with precondition: [0>=A,B=0] 

* Chain [[15],19]...: 3*it(15)+0
  with precondition: [B=0,G=3,0>=A] 

* Chain [[15],18]: 2*it(15)+0
  with precondition: [B=0,G=3,0>=A] 

* Chain [[15],17]: 3*it(15)+0
  with precondition: [B=0,G=3,0>=A] 

* Chain [[15],16]: 2*it(15)+0
  with precondition: [B=0,G=4,I=0,0>=A,H>=1,J>=1] 

* Chain [19]...: 1*s(5)+0
  with precondition: [B=0,G=3,0>=A] 

* Chain [18]: 0
  with precondition: [B=0,G=3] 

* Chain [17]: 1*s(6)+0
  with precondition: [B=0,G=3,0>=A] 

* Chain [16]: 0
  with precondition: [B=0,G=4,I=0,J=C,K=D,L=E,A=H,A>=1] 


#### Cost of chains of f25(G):
* Chain [[20]]...: 1*it(20)+0
  with precondition: [G=3] 

* Chain [[20],21]: 1*it(20)+0
  with precondition: [G=3] 

* Chain [21]: 0
  with precondition: [G=3] 


#### Cost of chains of f10_loop_cont(A,B,C,D,E,F,G):
* Chain [24]...: 1*s(13)+0
  with precondition: [A=4] 

* Chain [23]: 0
  with precondition: [A=3] 

* Chain [22]: 1*s(14)+0
  with precondition: [A=4] 


#### Cost of chains of f0(A,B,C,D,E,G):
* Chain [26]: 1*aux(5)+0
  with precondition: [] 

* Chain [25]...: 1*aux(6)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,G): 
-------------------------------------
* Chain [26] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [25]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,E,G): inf 
Asymptotic class: infinity 
* Total analysis performed in 86 ms.

