WARNING: Excluded non-linear constraints:[G=5*A+C*C,A+1=<B*B]

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

#### Computed strongly connected components 
0. recursive  : [l2/6]
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 l2/6
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 l2/6 
* 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 l2/6 
* CEs [11] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR l2(A,B,C,F,G,H) 

#### Partial ranking functions of CR l2(A,B,C,F,G,H) 


### Specialization of cost equations l1/7 
* CE 2 is refined into CE [12,13,14] 
* CE 5 is refined into CE [15] 
* CE 4 is refined into CE [16] 
* CE 3 is refined into CE [17,18,19] 


### Cost equations --> "Loop" of l1/7 
* CEs [19] --> Loop 12 
* CEs [16] --> Loop 13 
* CEs [17] --> Loop 14 
* CEs [18] --> Loop 15 
* CEs [15] --> Loop 16 
* CEs [12] --> Loop 17 
* CEs [13] --> Loop 18 
* CEs [14] --> Loop 19 

### 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 [12:1,14:1]:
    A depends on loops [13:1,15:1] 
  - RF of loop [13:1]:
    C depends on loops [12:1,14:1,15:1] 
  - RF of loop [14:1,15:1]:
    -C+1 depends on loops [12:1,13:1] 
    F depends on loops [12:1] 


### Specialization of cost equations l0/7 
* CE 1 is refined into CE [20,21,22,23,24,25,26] 


### Cost equations --> "Loop" of l0/7 
* CEs [24,26] --> Loop 20 
* CEs [25] --> Loop 21 
* CEs [22,23] --> Loop 22 
* CEs [21] --> Loop 23 
* CEs [20] --> Loop 24 

### 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,F,G,H):
* Chain [[9]]...: 1*it(9)+0
  with precondition: [A>=1,0>=C,G>=2,3>=G] 

* Chain [[9],11]: 1*it(9)+0
  with precondition: [G=2,H+1=F,0>=C,A>=1,H>=0] 

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

* Chain [11]: 0
  with precondition: [G=2,F=H+1,0>=C,F>=1] 

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


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

* Chain [[12,13,14,15],19]...: 7*it(12)+0
  with precondition: [G=3,B=E,A>=D] 

* Chain [[12,13,14,15],18]: 7*it(12)+0
  with precondition: [G=3,B=E,A>=D] 

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

* Chain [[12,13,14,15],16]: 6*it(12)+0
  with precondition: [G=3,B=E,A>=D] 

* Chain [19]...: 1*s(7)+0
  with precondition: [G=3,E=B,0>=C,A>=1,A>=D] 

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

* Chain [17]: 0
  with precondition: [G=3,E=B,0>=C,A>=D] 

* Chain [16]: 0
  with precondition: [G=3,E=B,A>=D] 


#### Cost of chains of l0(A,B,C,D,E,F,G):
* Chain [24]: 1*s(12)+0
  with precondition: [0>=C,D>=1,F>=1] 

* Chain [23]: 0
  with precondition: [0>=C,F>=1] 

* Chain [22]: 1*aux(227)+0
  with precondition: [F>=1] 

* Chain [21]...: 1*s(14)+0
  with precondition: [0>=C,D>=1,F>=1] 

* Chain [20]...: 1*aux(228)+0
  with precondition: [F>=1] 


Closed-form bounds of l0(A,B,C,D,E,F,G): 
-------------------------------------
* Chain [24] with precondition: [0>=C,D>=1,F>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [23] with precondition: [0>=C,F>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [22] with precondition: [F>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [21]... with precondition: [0>=C,D>=1,F>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [20]... with precondition: [F>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,C,D,E,F,G): inf 
Asymptotic class: infinity 
* Total analysis performed in 817 ms.

