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

#### Computed strongly connected components 
0. recursive  : [f4/14]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f6/8]
3. non_recursive  : [f4_loop_cont/9]
4. non_recursive  : [f5/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f4/14
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f4_loop_cont/9
4. SCC is partially evaluated into f5/8

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

### Specialization of cost equations f4/14 
* CE 5 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10] 


### Cost equations --> "Loop" of f4/14 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

### Ranking functions of CR f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 

#### Partial ranking functions of CR f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N) 


### Specialization of cost equations f4_loop_cont/9 
* CE 7 is refined into CE [11] 
* CE 6 is refined into CE [12] 


### Cost equations --> "Loop" of f4_loop_cont/9 
* CEs [11] --> Loop 11 
* CEs [12] --> Loop 12 

### Ranking functions of CR f4_loop_cont(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR f4_loop_cont(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations f5/8 
* CE 1 is refined into CE [13] 
* CE 2 is refined into CE [14,15,16,17,18] 


### Cost equations --> "Loop" of f5/8 
* CEs [17,18] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [16] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [14] --> Loop 17 

### Ranking functions of CR f5(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR f5(A,B,C,D,E,F,G,H) 


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

#### Cost of chains of f4(A,B,C,D,E,F,G,H,I,J,K,L,M,N):
* Chain [[8]]...: 1*it(8)+0
  with precondition: [0>=B+1,A>=0] 

* Chain [[8],9]: 1*it(8)+0
  with precondition: [H=3,0>=B+1,A>=0] 

* Chain [10]: 0
  with precondition: [H=2,J=0,K=0,L=0,M=0,N=0,A=I,0>=A+1,0>=B+1] 

* Chain [9]: 0
  with precondition: [H=3,0>=B+1] 


#### Cost of chains of f4_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [12]: 0
  with precondition: [A=2,0>=C+1] 

* Chain [11]: 0
  with precondition: [A=3,0>=C+1] 


#### Cost of chains of f5(A,B,C,D,E,F,G,H):
* Chain [17]: 0
  with precondition: [0>=A+1,0>=B+1] 

* Chain [16]: 0
  with precondition: [0>=B+1] 

* Chain [15]: 1*s(1)+0
  with precondition: [0>=B+1,A>=0] 

* Chain [14]: 0
  with precondition: [B>=0] 

* Chain [13]...: 1*aux(1)+0
  with precondition: [0>=B+1,A>=0] 


Closed-form bounds of f5(A,B,C,D,E,F,G,H): 
-------------------------------------
* Chain [17] with precondition: [0>=A+1,0>=B+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [0>=B+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [0>=B+1,A>=0] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [14] with precondition: [B>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [13]... with precondition: [0>=B+1,A>=0] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f5(A,B,C,D,E,F,G,H): inf 
Asymptotic class: infinity 
* Total analysis performed in 68 ms.

