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

#### Computed strongly connected components 
0. recursive  : [l1/5]
1. non_recursive  : [exit_location/1]
2. recursive  : [l2/3]
3. non_recursive  : [l2_loop_cont/2]
4. non_recursive  : [l1_loop_cont/6]
5. non_recursive  : [l0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l1/5
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into l2/3
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into l1_loop_cont/6
5. SCC is partially evaluated into l0/5

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

### Specialization of cost equations l1/5 
* 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 l1/5 
* CEs [11] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR l1(X1,X2,Z2,A3,B3) 

#### Partial ranking functions of CR l1(X1,X2,Z2,A3,B3) 


### Specialization of cost equations l2/3 
* CE 8 is refined into CE [12] 
* CE 7 is refined into CE [13] 


### Cost equations --> "Loop" of l2/3 
* CEs [13] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR l2(Y1,Y2,Z2) 

#### Partial ranking functions of CR l2(Y1,Y2,Z2) 


### Specialization of cost equations l1_loop_cont/6 
* CE 6 is refined into CE [14,15,16] 
* CE 5 is refined into CE [17] 


### Cost equations --> "Loop" of l1_loop_cont/6 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [17] --> Loop 16 
* CEs [16] --> Loop 17 

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

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


### Specialization of cost equations l0/5 
* CE 1 is refined into CE [18,19,20,21,22,23,24,25,26,27,28,29] 


### Cost equations --> "Loop" of l0/5 
* CEs [22] --> Loop 18 
* CEs [26,27] --> Loop 19 
* CEs [25,28,29] --> Loop 20 
* CEs [21] --> Loop 21 
* CEs [19,23] --> Loop 22 
* CEs [24] --> Loop 23 
* CEs [18,20] --> Loop 24 

### Ranking functions of CR l0(X1,X2,Y1,Y2,Z2) 

#### Partial ranking functions of CR l0(X1,X2,Y1,Y2,Z2) 


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

#### Cost of chains of l1(X1,X2,Z2,A3,B3):
* Chain [[9]]...: 1*it(9)+0
  with precondition: [X1>=X2+1,X2>=1] 

* Chain [[9],11]: 1*it(9)+0
  with precondition: [Z2=2,X2>=1,X1>=X2+1] 

* Chain [[9],10]: 1*it(9)+0
  with precondition: [Z2=3,X2>=1,B3>=3*X2,3*A3>=2*B3+6,X1>=X2+1,2*A3+3*X2>=4*X1+B3] 

* Chain [11]: 0
  with precondition: [Z2=2] 

* Chain [10]: 0
  with precondition: [Z2=3,A3=X1,B3=X2] 


#### Cost of chains of l2(Y1,Y2,Z2):
* Chain [[12]]...: 1*it(12)+0
  with precondition: [Y1>=1,Z2=2] 

* Chain [[12],13]: 1*it(12)+0
  with precondition: [Z2=2,Y1>=1] 

* Chain [13]: 0
  with precondition: [Z2=2] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F):
* Chain [17]...: 1*s(1)+0
  with precondition: [A=3,D>=1] 

* Chain [16]: 0
  with precondition: [A=2] 

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

* Chain [14]: 1*s(2)+0
  with precondition: [A=3,D>=1] 


#### Cost of chains of l0(X1,X2,Y1,Y2,Z2):
* Chain [24]: 0
  with precondition: [] 

* Chain [23]: 2*s(3)+0
  with precondition: [X2>=1,Y1>=1,X1>=X2+1] 

* Chain [22]: 1*aux(1)+0
  with precondition: [X2>=1,X1>=X2+1] 

* Chain [21]: 1*s(7)+0
  with precondition: [Y1>=1] 

* Chain [20]...: 1*aux(2)+0
  with precondition: [X2>=1,Y1>=1,X1>=X2+1] 

* Chain [19]...: 1*aux(3)+0
  with precondition: [X2>=1,X1>=X2+1] 

* Chain [18]...: 1*s(16)+0
  with precondition: [Y1>=1] 


Closed-form bounds of l0(X1,X2,Y1,Y2,Z2): 
-------------------------------------
* Chain [24] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [23] with precondition: [X2>=1,Y1>=1,X1>=X2+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [22] with precondition: [X2>=1,X1>=X2+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [21] with precondition: [Y1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [20]... with precondition: [X2>=1,Y1>=1,X1>=X2+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [19]... with precondition: [X2>=1,X1>=X2+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [18]... with precondition: [Y1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(X1,X2,Y1,Y2,Z2): inf 
Asymptotic class: infinity 
* Total analysis performed in 55 ms.

