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

#### Computed strongly connected components 
0. recursive  : [f300/7]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f1/4]
3. non_recursive  : [f300_loop_cont/5]
4. non_recursive  : [f2/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f300/7
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f300_loop_cont/5
4. SCC is partially evaluated into f2/4

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

### Specialization of cost equations f300/7 
* CE 5 is refined into CE [8] 
* CE 4 is refined into CE [9] 
* CE 3 is refined into CE [10] 
* CE 2 is refined into CE [11] 


### Cost equations --> "Loop" of f300/7 
* CEs [11] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR f300(A,B,C,E,F,G,H) 
* RF of phase [8]: [A]

#### Partial ranking functions of CR f300(A,B,C,E,F,G,H) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    A


### Specialization of cost equations f300_loop_cont/5 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 


### Cost equations --> "Loop" of f300_loop_cont/5 
* CEs [12] --> Loop 12 
* CEs [13] --> Loop 13 

### Ranking functions of CR f300_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f300_loop_cont(A,B,C,D,E) 


### Specialization of cost equations f2/4 
* CE 1 is refined into CE [14,15,16,17,18] 


### Cost equations --> "Loop" of f2/4 
* CEs [16,18] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [17] --> Loop 17 

### Ranking functions of CR f2(A,B,C,E) 

#### Partial ranking functions of CR f2(A,B,C,E) 


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

#### Cost of chains of f300(A,B,C,E,F,G,H):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< A
it(8) =< A-F

  with precondition: [E=2,F=G+1,1>=F,A>=1,B>=1,A>=F+1] 

* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< A

  with precondition: [E=3,A>=1,B>=1] 

* Chain [11]: 0
  with precondition: [E=2,A=F,B=G,0>=A,B>=1] 

* Chain [10]: 0
  with precondition: [E=2,F=A,B=G,0>=B] 

* Chain [9]: 0
  with precondition: [E=3] 


#### Cost of chains of f300_loop_cont(A,B,C,D,E):
* Chain [13]: 0
  with precondition: [A=2] 

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


#### Cost of chains of f2(A,B,C,E):
* Chain [17]: 0
  with precondition: [] 

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

* Chain [15]: 0
  with precondition: [0>=B] 

* Chain [14]: 2*s(1)+0
  Such that:aux(1) =< A
s(1) =< aux(1)

  with precondition: [A>=1,B>=1] 


Closed-form bounds of f2(A,B,C,E): 
-------------------------------------
* Chain [17] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [0>=A,B>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [0>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [14] with precondition: [A>=1,B>=1] 
    - Upper bound: 2*A 
    - Complexity: n 

### Maximum cost of f2(A,B,C,E): nat(A)*2 
Asymptotic class: n 
* Total analysis performed in 41 ms.

