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

#### Computed strongly connected components 
0. recursive  : [l1/10,l2/10,l3/10]
1. non_recursive  : [exit_location/1]
2. recursive  : [l4/2]
3. non_recursive  : [l4_loop_cont/2]
4. non_recursive  : [l1_loop_cont/7]
5. non_recursive  : [l0/6]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l1/10
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into l4/2
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into l1_loop_cont/7
5. SCC is partially evaluated into l0/6

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

### Specialization of cost equations l1/10 
* CE 4 is refined into CE [10] 
* CE 5 is refined into CE [11] 
* CE 2 is refined into CE [12] 
* CE 3 is refined into CE [13] 


### Cost equations --> "Loop" of l1/10 
* CEs [12] --> Loop 10 
* CEs [13] --> Loop 11 
* CEs [10] --> Loop 12 
* CEs [11] --> Loop 13 

### Ranking functions of CR l1(A,B,C,D,E,F,G,H,I,J) 
* RF of phase [10,11]: [E]

#### Partial ranking functions of CR l1(A,B,C,D,E,F,G,H,I,J) 
* Partial RF of phase [10,11]:
  - RF of loop [10:1,11:1]:
    E


### Specialization of cost equations l4/2 
* CE 9 is refined into CE [14] 
* CE 8 is refined into CE [15] 


### Cost equations --> "Loop" of l4/2 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR l4(A,F) 
* RF of phase [14]: [A+1]

#### Partial ranking functions of CR l4(A,F) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    A+1


### Specialization of cost equations l1_loop_cont/7 
* CE 7 is refined into CE [16,17] 
* CE 6 is refined into CE [18] 


### Cost equations --> "Loop" of l1_loop_cont/7 
* CEs [17] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [18] --> Loop 18 

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

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


### Specialization of cost equations l0/6 
* CE 1 is refined into CE [19,20,21,22,23,24] 


### Cost equations --> "Loop" of l0/6 
* CEs [20,21,22] --> Loop 19 
* CEs [24] --> Loop 20 
* CEs [23] --> Loop 21 
* CEs [19] --> Loop 22 

### Ranking functions of CR l0(A,B,C,D,E,F) 

#### Partial ranking functions of CR l0(A,B,C,D,E,F) 


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

#### Cost of chains of l1(A,B,C,D,E,F,G,H,I,J):
* Chain [[10,11],13]: 2*it(10)+0
  Such that:aux(3) =< E
it(10) =< aux(3)

  with precondition: [F=2,E>=1] 

* Chain [[10,11],12]: 2*it(10)+0
  Such that:aux(4) =< E
it(10) =< aux(4)

  with precondition: [F=3,J=0,G=H+I,E>=1] 

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

* Chain [12]: 0
  with precondition: [F=3,G=A,H=C,I=D,E=J,0>=E] 


#### Cost of chains of l4(A,F):
* Chain [[14],15]: 1*it(14)+0
  Such that:it(14) =< A+1

  with precondition: [F=2,A>=0] 

* Chain [15]: 0
  with precondition: [F=2] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F,G):
* Chain [18]: 0
  with precondition: [A=2] 

* Chain [17]: 0
  with precondition: [A=3] 

* Chain [16]: 1*s(1)+0
  Such that:s(1) =< B+1

  with precondition: [A=3,B>=0] 


#### Cost of chains of l0(A,B,C,D,E,F):
* Chain [22]: 0
  with precondition: [] 

* Chain [21]: 0
  with precondition: [0>=E] 

* Chain [20]: 1*s(2)+0
  Such that:s(2) =< A+1

  with precondition: [0>=E,A>=0] 

* Chain [19]: 6*s(4)+1*s(9)+0
  Such that:aux(5) =< E
s(4) =< aux(5)

  with precondition: [E>=1] 


Closed-form bounds of l0(A,B,C,D,E,F): 
-------------------------------------
* Chain [22] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [21] with precondition: [0>=E] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [20] with precondition: [0>=E,A>=0] 
    - Upper bound: A+1 
    - Complexity: n 
* Chain [19] with precondition: [E>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,C,D,E,F): inf 
Asymptotic class: infinity 
* Total analysis performed in 80 ms.

