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

#### Computed strongly connected components 
0. recursive  : [f12/14,f6/14]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f20/8]
3. non_recursive  : [f6_loop_cont/9]
4. non_recursive  : [f0/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f6/14
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f6_loop_cont/9
4. SCC is partially evaluated into f0/8

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

### Specialization of cost equations f6/14 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 
* CE 2 is refined into CE [11] 
* CE 3 is refined into CE [12] 
* CE 4 is refined into CE [13] 


### Cost equations --> "Loop" of f6/14 
* CEs [13] --> Loop 9 
* CEs [11] --> Loop 10 
* CEs [12] --> Loop 11 
* CEs [9] --> Loop 12 
* CEs [10] --> Loop 13 

### Ranking functions of CR f6(A,B,C,D,E,F,G,J,K,L,M,N,O,P) 

#### Partial ranking functions of CR f6(A,B,C,D,E,F,G,J,K,L,M,N,O,P) 


### Specialization of cost equations f6_loop_cont/9 
* CE 8 is refined into CE [14] 
* CE 7 is refined into CE [15] 


### Cost equations --> "Loop" of f6_loop_cont/9 
* CEs [14] --> Loop 14 
* CEs [15] --> Loop 15 

### Ranking functions of CR f6_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f6_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f0/8 
* CE 1 is refined into CE [16,17,18,19,20,21,22] 


### Cost equations --> "Loop" of f0/8 
* CEs [21,22] --> Loop 16 
* CEs [16,17,18,19,20] --> Loop 17 

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

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


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

#### Cost of chains of f6(A,B,C,D,E,F,G,J,K,L,M,N,O,P):
* Chain [[10,11]]...: 2*it(10)+0
  with precondition: [A=8,C>=B,D+1=0] 

* Chain [[10,11],13]: 2*it(10)+0
  with precondition: [A=8,D+1=0,J=2,M+1=0,O+1=0,P+1=0,C>=B,K>=L+1,N>=L,K>=N] 

* Chain [[10,11],12]: 2*it(10)+0
  with precondition: [A=8,D+1=0,J=3,C>=B] 

* Chain [[10,11],9,13]: 2*it(10)+1
  with precondition: [A=8,D+1=0,J=2,K=L+1,M=O,M=P,C>=B] 

* Chain [[10,11],9,12]: 2*it(10)+1
  with precondition: [A=8,D+1=0,J=3,C>=B] 

* Chain [12]: 0
  with precondition: [A=8,J=3] 

* Chain [9,13]: 1
  with precondition: [A=8,D+1=0,J=2,B=K,B=L+1,M=O,M=P,C>=B] 

* Chain [9,12]: 1
  with precondition: [A=8,D+1=0,J=3,C>=B] 


#### Cost of chains of f6_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [15]: 0
  with precondition: [A=2,B=8] 

* Chain [14]: 0
  with precondition: [A=3,B=8] 


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

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


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

### Maximum cost of f0(A,B,C,D,E,F,G,J): inf 
Asymptotic class: infinity 
* Total analysis performed in 126 ms.

