WARNING: Excluded non-linear constraints:[M=5*E-A*A,B*B>=1+1,A*C+2*A>=0+1]

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

#### Computed strongly connected components 
0. recursive  : [l2/12]
1. recursive  : [l1/7,l2_loop_cont/8]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [l1_loop_cont/2]
4. non_recursive  : [l0/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l2/12
1. SCC is partially evaluated into l1/7
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into l0/7

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

### Specialization of cost equations l2/12 
* CE 8 is refined into CE [9] 
* CE 7 is refined into CE [10] 
* CE 6 is refined into CE [11] 


### Cost equations --> "Loop" of l2/12 
* CEs [11] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR l2(A,B,C,D,E,F,G,H,I,J,K,L) 

#### Partial ranking functions of CR l2(A,B,C,D,E,F,G,H,I,J,K,L) 


### Specialization of cost equations l1/7 
* CE 2 is refined into CE [12,13] 
* CE 5 is refined into CE [14] 
* CE 3 is refined into CE [15,16,17] 
* CE 4 is refined into CE [18] 


### Cost equations --> "Loop" of l1/7 
* CEs [18] --> Loop 12 
* CEs [16] --> Loop 13 
* CEs [15] --> Loop 14 
* CEs [17] --> Loop 15 
* CEs [12] --> Loop 16 
* CEs [14] --> Loop 17 
* CEs [13] --> Loop 18 

### Ranking functions of CR l1(A,B,C,D,E,F,G) 

#### Partial ranking functions of CR l1(A,B,C,D,E,F,G) 
* Partial RF of phase [12,13,14,15]:
  - RF of loop [12:1]:
    C depends on loops [13:1,14:1,15:1] 
  - RF of loop [13:1,14:1]:
    -C+1 depends on loops [12:1,15:1] 
    F depends on loops [15:1] 


### Specialization of cost equations l0/7 
* CE 1 is refined into CE [19,20,21,22] 


### Cost equations --> "Loop" of l0/7 
* CEs [22] --> Loop 19 
* CEs [21] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [19] --> Loop 22 

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

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


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

#### Cost of chains of l2(A,B,C,D,E,F,G,H,I,J,K,L):
* Chain [[9]]...: 1*it(9)+0
  with precondition: [G>=2,3>=G] 

* Chain [[9],11]: 1*it(9)+0
  with precondition: [G=2,H=J,I=K,F=L+1,F>=1] 

* Chain [[9],10]: 1*it(9)+0
  with precondition: [G=3] 

* Chain [11]: 0
  with precondition: [G=2,D=H,E=I,D=J,E=K,F=L+1,F>=1] 

* Chain [10]: 0
  with precondition: [G=3] 


#### Cost of chains of l1(A,B,C,D,E,F,G):
* Chain [[12,13,14,15]]...: 6*it(12)+0
  with precondition: [G=3] 

* Chain [[12,13,14,15],18]...: 7*it(12)+0
  with precondition: [G=3] 

* Chain [[12,13,14,15],17]: 6*it(12)+0
  with precondition: [G=3] 

* Chain [[12,13,14,15],16]: 7*it(12)+0
  with precondition: [G=3] 

* Chain [18]...: 1*s(8)+0
  with precondition: [G=3,0>=C] 

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

* Chain [16]: 1*s(9)+0
  with precondition: [G=3,0>=C] 


#### Cost of chains of l0(A,B,C,D,E,F,G):
* Chain [22]: 1*s(14)+0
  with precondition: [] 

* Chain [21]: 1*s(15)+0
  with precondition: [0>=F] 

* Chain [20]...: 1*s(16)+0
  with precondition: [] 

* Chain [19]...: 1*s(17)+0
  with precondition: [0>=F] 


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

### Maximum cost of l0(A,B,C,D,E,F,G): inf 
Asymptotic class: infinity 
* Total analysis performed in 124 ms.

