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

#### Computed strongly connected components 
0. recursive  : [l1/12,l2/12]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [l3/8]
3. non_recursive  : [l1_loop_cont/9]
4. non_recursive  : [l0/8]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l1/12
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into l1_loop_cont/9
4. SCC is partially evaluated into l0/8

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

### Specialization of cost equations l1/12 
* CE 2 is refined into CE [8] 
* CE 5 is refined into CE [9] 
* CE 4 is refined into CE [10] 
* CE 3 is refined into CE [11] 


### Cost equations --> "Loop" of l1/12 
* CEs [10] --> Loop 8 
* CEs [11] --> Loop 9 
* CEs [8] --> Loop 10 
* CEs [9] --> Loop 11 

### Ranking functions of CR l1(A,B,C,F,X,Y,Z,A1,B1,C1,D1,E1) 

#### Partial ranking functions of CR l1(A,B,C,F,X,Y,Z,A1,B1,C1,D1,E1) 
* Partial RF of phase [8,9]:
  - RF of loop [9:1]:
    F-1


### Specialization of cost equations l1_loop_cont/9 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 


### Cost equations --> "Loop" of l1_loop_cont/9 
* CEs [12] --> Loop 12 
* CEs [13] --> Loop 13 

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

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


### Specialization of cost equations l0/8 
* CE 1 is refined into CE [14,15,16,17,18] 


### Cost equations --> "Loop" of l0/8 
* CEs [17,18] --> Loop 14 
* CEs [15] --> Loop 15 
* CEs [14,16] --> Loop 16 

### Ranking functions of CR l0(A,B,C,F,X,Y,Z,A1) 

#### Partial ranking functions of CR l0(A,B,C,F,X,Y,Z,A1) 


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

#### Cost of chains of l1(A,B,C,F,X,Y,Z,A1,B1,C1,D1,E1):
* Chain [[8,9]]...: 1*it(8)+1*it(9)+0
  Such that:it(9) =< F

  with precondition: [Z>=C] 

* Chain [[8,9],11]: 1*it(8)+1*it(9)+0
  Such that:it(9) =< F

  with precondition: [A1=2,Z>=C] 

* Chain [[8,9],10]: 1*it(8)+1*it(9)+0
  Such that:it(9) =< F
it(9) =< F-E1

  with precondition: [A1=3,0>=B1,0>=E1,Z>=C,Z>=D1,F>=E1+1,F+Z>=D1+E1+2] 

* Chain [11]: 0
  with precondition: [A1=2,Z>=C] 

* Chain [10]: 0
  with precondition: [A1=3,C1=B,E1+1=F,A=B1,C=D1,0>=A,0>=E1,Z>=C] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F,G,H,I):
* Chain [13]: 0
  with precondition: [A=2] 

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


#### Cost of chains of l0(A,B,C,F,X,Y,Z,A1):
* Chain [16]: 2*s(3)+2*s(4)+0
  Such that:aux(1) =< F
s(3) =< aux(1)

  with precondition: [] 

* Chain [15]: 0
  with precondition: [1>=F,0>=X] 

* Chain [14]...: 2*s(7)+2*s(8)+0
  Such that:aux(2) =< F
s(7) =< aux(2)

  with precondition: [] 


Closed-form bounds of l0(A,B,C,F,X,Y,Z,A1): 
-------------------------------------
* Chain [16] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [15] with precondition: [1>=F,0>=X] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [14]... with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,C,F,X,Y,Z,A1): inf 
Asymptotic class: infinity 
* Total analysis performed in 81 ms.

