WARNING: Excluded non-linear constraints:[F=5*A+C*C]

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

#### Computed strongly connected components 
0. recursive  : [l2/5]
1. recursive  : [l1/6,l2_loop_cont/7]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [l1_loop_cont/2]
4. non_recursive  : [l0/6]

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

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

### Specialization of cost equations l2/5 
* CE 7 is refined into CE [8] 
* CE 6 is refined into CE [9] 
* CE 5 is refined into CE [10] 


### Cost equations --> "Loop" of l2/5 
* CEs [10] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 

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

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


### Specialization of cost equations l1/6 
* CE 2 is refined into CE [11,12,13] 
* CE 4 is refined into CE [14] 
* CE 3 is refined into CE [15,16,17] 


### Cost equations --> "Loop" of l1/6 
* CEs [17] --> Loop 11 
* CEs [16] --> Loop 12 
* CEs [15] --> Loop 13 
* CEs [12] --> Loop 14 
* CEs [11] --> Loop 15 
* CEs [14] --> Loop 16 
* CEs [13] --> Loop 17 

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

#### Partial ranking functions of CR l1(A,B,C,D,E,F) 
* Partial RF of phase [11,12,13]:
  - RF of loop [12:1,13:1]:
    C depends on loops [11:1] 


### Specialization of cost equations l0/6 
* CE 1 is refined into CE [18,19,20,21,22,23,24,25] 


### Cost equations --> "Loop" of l0/6 
* CEs [24,25] --> Loop 18 
* CEs [23] --> Loop 19 
* CEs [20,21] --> Loop 20 
* CEs [19,22] --> Loop 21 
* CEs [18] --> 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 l2(A,B,C,F,G):
* Chain [[8]]...: 1*it(8)+0
  with precondition: [B>=A+1,A>=1,C>=1,F>=2,3>=F] 

* Chain [[8],10]: 1*it(8)+0
  with precondition: [F=2,C=G+1,A>=1,C>=1,B>=A+1] 

* Chain [[8],9]: 1*it(8)+0
  with precondition: [F=3,A>=1,C>=1,B>=A+1] 

* Chain [10]: 0
  with precondition: [F=2,C=G+1,C>=1] 

* Chain [9]: 0
  with precondition: [F=3,C>=1] 


#### Cost of chains of l1(A,B,C,D,E,F):
* Chain [[11,12,13]]...: 5*it(11)+0
  with precondition: [B=E,A=D,C>=1,F=3] 

* Chain [[11,12,13],17]...: 6*it(11)+0
  with precondition: [F=3,A=D,B=E,A>=1,C>=1,B>=A+1] 

* Chain [[11,12,13],16]: 5*it(11)+0
  with precondition: [F=3,A=D,B=E,C>=1] 

* Chain [[11,12,13],15]: 6*it(11)+0
  with precondition: [F=3,A=D,B=E,A>=1,C>=1,B>=A+1] 

* Chain [[11,12,13],14]: 5*it(11)+0
  with precondition: [F=3,A=D,B=E,C>=1] 

* Chain [17]...: 1*s(7)+0
  with precondition: [F=3,D=A,E=B,C>=1,D>=1,E>=D+1] 

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

* Chain [15]: 1*s(8)+0
  with precondition: [F=3,D=A,E=B,C>=1,D>=1,E>=D+1] 

* Chain [14]: 0
  with precondition: [F=3,D=A,E=B,C>=1] 


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

* Chain [21]: 1*aux(2)+0
  with precondition: [C>=1] 

* Chain [20]: 1*aux(3)+0
  with precondition: [C>=1,D>=1,E>=D+1] 

* Chain [19]...: 5*s(14)+0
  with precondition: [C>=1] 

* Chain [18]...: 1*aux(4)+0
  with precondition: [C>=1,D>=1,E>=D+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: [C>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [20] with precondition: [C>=1,D>=1,E>=D+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [19]... with precondition: [C>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [18]... with precondition: [C>=1,D>=1,E>=D+1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,C,D,E,F): inf 
Asymptotic class: infinity 
* Total analysis performed in 91 ms.

