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

#### Computed strongly connected components 
0. recursive  : [f14/7]
1. recursive  : [f14_loop_cont/10,f9/9]
2. non_recursive  : [exit_location/1]
3. recursive  : [f22/1]
4. non_recursive  : [f22_loop_cont/2]
5. non_recursive  : [f9_loop_cont/6]
6. non_recursive  : [f0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f14/7
1. SCC is partially evaluated into f9/9
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f22/1
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into f9_loop_cont/6
6. SCC is partially evaluated into f0/5

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

### Specialization of cost equations f14/7 
* CE 10 is refined into CE [13] 
* CE 9 is refined into CE [14] 
* CE 8 is refined into CE [15] 


### Cost equations --> "Loop" of f14/7 
* CEs [15] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR f14(A,C,D,F,G,H,I) 
* RF of phase [13]: [C]

#### Partial ranking functions of CR f14(A,C,D,F,G,H,I) 
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    C


### Specialization of cost equations f9/9 
* CE 4 is refined into CE [16] 
* CE 2 is refined into CE [17,18] 
* CE 5 is refined into CE [19] 
* CE 3 is refined into CE [20,21] 


### Cost equations --> "Loop" of f9/9 
* CEs [21] --> Loop 16 
* CEs [20] --> Loop 17 
* CEs [16] --> Loop 18 
* CEs [17,18] --> Loop 19 
* CEs [19] --> Loop 20 

### Ranking functions of CR f9(A,B,C,D,F,G,H,I,J) 

#### Partial ranking functions of CR f9(A,B,C,D,F,G,H,I,J) 


### Specialization of cost equations f22/1 
* CE 12 is refined into CE [22] 
* CE 11 is refined into CE [23] 


### Cost equations --> "Loop" of f22/1 
* CEs [23] --> Loop 21 
* CEs [22] --> Loop 22 

### Ranking functions of CR f22(F) 

#### Partial ranking functions of CR f22(F) 


### Specialization of cost equations f9_loop_cont/6 
* CE 7 is refined into CE [24,25] 
* CE 6 is refined into CE [26] 


### Cost equations --> "Loop" of f9_loop_cont/6 
* CEs [24] --> Loop 23 
* CEs [26] --> Loop 24 
* CEs [25] --> Loop 25 

### Ranking functions of CR f9_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR f9_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations f0/5 
* CE 1 is refined into CE [27,28,29,30,31,32,33,34,35] 


### Cost equations --> "Loop" of f0/5 
* CEs [30,32,33,34,35] --> Loop 26 
* CEs [27,28,29,31] --> Loop 27 

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

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


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

#### Cost of chains of f14(A,C,D,F,G,H,I):
* Chain [[13],15]: 1*it(13)+0
  Such that:it(13) =< C

  with precondition: [F=2,H=0,I=0,0>=A,C>=1] 

* Chain [[13],14]: 1*it(13)+0
  Such that:it(13) =< C

  with precondition: [F=3,0>=A,C>=1] 

* Chain [15]: 0
  with precondition: [F=2,I=0,C=H,0>=A,0>=C] 

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


#### Cost of chains of f9(A,B,C,D,F,G,H,I,J):
* Chain [[16,17]]...: 3*it(16)+0
  with precondition: [0>=A,B=0] 

* Chain [[16,17],20]: 3*it(16)+0
  with precondition: [B=0,D=0,F=3,0>=A] 

* Chain [[16,17],19]: 4*aux(1)+0
  with precondition: [B=0,D=0,F=3,0>=A] 

* Chain [[16,17],18]: 3*it(16)+0
  with precondition: [B=0,D=0,F=4,H=0,J=0,0>=A,0>=I,G>=1] 

* Chain [20]: 0
  with precondition: [B=0,D=0,F=3] 

* Chain [19]: 1*aux(1)+0
  with precondition: [B=0,D=0,F=3,0>=A] 

* Chain [18]: 0
  with precondition: [B=0,D=0,F=4,H=0,J=0,I=C,A=G,A>=1] 


#### Cost of chains of f22(F):
* Chain [[21]]...: 1*it(21)+0
  with precondition: [F=3] 

* Chain [[21],22]: 1*it(21)+0
  with precondition: [F=3] 

* Chain [22]: 0
  with precondition: [F=3] 


#### Cost of chains of f9_loop_cont(A,B,C,D,E,F):
* Chain [25]...: 1*s(9)+0
  with precondition: [A=4] 

* Chain [24]: 0
  with precondition: [A=3] 

* Chain [23]: 1*s(10)+0
  with precondition: [A=4] 


#### Cost of chains of f0(A,B,C,D,F):
* Chain [27]: 1*aux(4)+0
  with precondition: [] 

* Chain [26]...: 1*aux(5)+0
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,F): 
-------------------------------------
* Chain [27] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [26]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,F): inf 
Asymptotic class: infinity 
* Total analysis performed in 88 ms.

