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

#### Computed strongly connected components 
0. recursive  : [l1/7]
1. non_recursive  : [exit_location/1]
2. recursive  : [l2/2]
3. non_recursive  : [l2_loop_cont/2]
4. non_recursive  : [l1_loop_cont/5]
5. non_recursive  : [l0/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l1/7
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into l2/2
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into l1_loop_cont/5
5. SCC is partially evaluated into l0/4

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

### Specialization of cost equations l1/7 
* CE 3 is refined into CE [9] 
* CE 4 is refined into CE [10] 
* CE 2 is refined into CE [11] 


### Cost equations --> "Loop" of l1/7 
* CEs [11] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR l1(X1,X2,X3,Y3,Z3,A4,B4) 
* RF of phase [9]: [X3]

#### Partial ranking functions of CR l1(X1,X2,X3,Y3,Z3,A4,B4) 
* Partial RF of phase [9]:
  - RF of loop [9:1]:
    X3


### Specialization of cost equations l2/2 
* CE 8 is refined into CE [12] 
* CE 7 is refined into CE [13] 


### Cost equations --> "Loop" of l2/2 
* CEs [13] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR l2(X1,Y3) 
* RF of phase [12]: [X1]

#### Partial ranking functions of CR l2(X1,Y3) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    X1


### Specialization of cost equations l1_loop_cont/5 
* CE 6 is refined into CE [14,15] 
* CE 5 is refined into CE [16] 


### Cost equations --> "Loop" of l1_loop_cont/5 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [16] --> Loop 16 

### Ranking functions of CR l1_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR l1_loop_cont(A,B,C,D,E) 


### Specialization of cost equations l0/4 
* CE 1 is refined into CE [17,18,19,20,21,22] 


### Cost equations --> "Loop" of l0/4 
* CEs [18,21,22] --> Loop 17 
* CEs [20] --> Loop 18 
* CEs [17,19] --> Loop 19 

### Ranking functions of CR l0(X1,X2,X3,Y3) 

#### Partial ranking functions of CR l0(X1,X2,X3,Y3) 


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

#### Cost of chains of l1(X1,X2,X3,Y3,Z3,A4,B4):
* Chain [[9],11]: 1*it(9)+0
  Such that:it(9) =< X3

  with precondition: [Y3=2,X3>=1] 

* Chain [[9],10]: 1*it(9)+0
  Such that:it(9) =< X3-B4

  with precondition: [Y3=3,B4>=0,X3>=B4+1] 

* Chain [11]: 0
  with precondition: [Y3=2] 

* Chain [10]: 0
  with precondition: [Y3=3,Z3=X1,A4=X2,B4=X3] 


#### Cost of chains of l2(X1,Y3):
* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< X1

  with precondition: [Y3=2,X1>=1] 

* Chain [13]: 0
  with precondition: [Y3=2] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E):
* Chain [16]: 0
  with precondition: [A=2] 

* Chain [15]: 0
  with precondition: [A=3] 

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

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


#### Cost of chains of l0(X1,X2,X3,Y3):
* Chain [19]: 0
  with precondition: [] 

* Chain [18]: 1*s(2)+0
  Such that:s(2) =< X1

  with precondition: [X1>=1] 

* Chain [17]: 3*s(3)+1*s(6)+0
  Such that:aux(1) =< X3
s(3) =< aux(1)

  with precondition: [X3>=1] 


Closed-form bounds of l0(X1,X2,X3,Y3): 
-------------------------------------
* Chain [19] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [18] with precondition: [X1>=1] 
    - Upper bound: X1 
    - Complexity: n 
* Chain [17] with precondition: [X3>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(X1,X2,X3,Y3): inf 
Asymptotic class: infinity 
* Total analysis performed in 45 ms.

