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

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

#### Computed strongly connected components 
0. recursive  : [l1/5]
1. non_recursive  : [exit_location/1]
2. recursive  : [l2/7]
3. recursive  : [l3/2]
4. non_recursive  : [l3_loop_cont/2]
5. non_recursive  : [l2_loop_cont/5]
6. non_recursive  : [l1_loop_cont/5]
7. non_recursive  : [l0/4]

#### 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 l2/7
3. SCC is partially evaluated into l3/2
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into l2_loop_cont/5
6. SCC is partially evaluated into l1_loop_cont/5
7. SCC is partially evaluated into l0/4

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

### Specialization of cost equations l1/5 
* CE 3 is refined into CE [14] 
* CE 4 is refined into CE [15] 
* CE 2 is refined into CE [16] 


### Cost equations --> "Loop" of l1/5 
* CEs [16] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR l1(A,C,D,E,F) 
* RF of phase [14]: [C]

#### Partial ranking functions of CR l1(A,C,D,E,F) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    C


### Specialization of cost equations l2/7 
* CE 8 is refined into CE [17] 
* CE 9 is refined into CE [18] 
* CE 7 is refined into CE [19] 


### Cost equations --> "Loop" of l2/7 
* CEs [19] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [18] --> Loop 19 

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

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


### Specialization of cost equations l3/2 
* CE 13 is refined into CE [20] 
* CE 12 is refined into CE [21] 


### Cost equations --> "Loop" of l3/2 
* CEs [21] --> Loop 20 
* CEs [20] --> Loop 21 

### Ranking functions of CR l3(A,D) 
* RF of phase [20]: [A]

#### Partial ranking functions of CR l3(A,D) 
* Partial RF of phase [20]:
  - RF of loop [20:1]:
    A


### Specialization of cost equations l2_loop_cont/5 
* CE 11 is refined into CE [22,23] 
* CE 10 is refined into CE [24] 


### Cost equations --> "Loop" of l2_loop_cont/5 
* CEs [23] --> Loop 22 
* CEs [22] --> Loop 23 
* CEs [24] --> Loop 24 

### Ranking functions of CR l2_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR l2_loop_cont(A,B,C,D,E) 


### Specialization of cost equations l1_loop_cont/5 
* CE 6 is refined into CE [25,26,27,28,29,30,31,32] 
* CE 5 is refined into CE [33] 


### Cost equations --> "Loop" of l1_loop_cont/5 
* CEs [27] --> Loop 25 
* CEs [25,26,28,29] --> Loop 26 
* CEs [33] --> Loop 27 
* CEs [30,31,32] --> Loop 28 

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

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


### Specialization of cost equations l0/4 
* CE 1 is refined into CE [34,35,36,37,38,39,40,41] 


### Cost equations --> "Loop" of l0/4 
* CEs [38] --> Loop 29 
* CEs [41] --> Loop 30 
* CEs [35,36,37] --> Loop 31 
* CEs [34] --> Loop 32 
* CEs [39,40] --> Loop 33 

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

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


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

#### Cost of chains of l1(A,C,D,E,F):
* Chain [[14],16]: 1*it(14)+0
  Such that:it(14) =< C

  with precondition: [D=2,A>=1,C>=1] 

* Chain [[14],15]: 1*it(14)+0
  Such that:it(14) =< C

  with precondition: [D=4,F=0,A>=1,C>=1] 

* Chain [16]: 0
  with precondition: [D=2,A>=1] 

* Chain [15]: 0
  with precondition: [D=4,A=E,C=F,0>=C,A>=1] 


#### Cost of chains of l2(A,B,C,D,E,F,G):
* Chain [[17]]...: 1*it(17)+0
  with precondition: [] 

* Chain [[17],19]: 1*it(17)+0
  with precondition: [D=2] 

* Chain [[17],18]: 1*it(17)+0
  with precondition: [D=3,B+G=C+F,F>=B+1] 

* Chain [19]: 0
  with precondition: [D=2] 

* Chain [18]: 0
  with precondition: [D=3,E=A,F=B,G=C] 


#### Cost of chains of l3(A,D):
* Chain [[20],21]: 1*it(20)+0
  Such that:it(20) =< A

  with precondition: [D=2,A>=1] 

* Chain [21]: 0
  with precondition: [D=2] 


#### Cost of chains of l2_loop_cont(A,B,C,D,E):
* Chain [24]: 0
  with precondition: [A=2] 

* Chain [23]: 0
  with precondition: [A=3] 

* Chain [22]: 1*s(2)+0
  Such that:s(2) =< B

  with precondition: [A=3,B>=1] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E):
* Chain [28]...: 1*aux(2)+0
  with precondition: [A=4] 

* Chain [27]: 0
  with precondition: [A=2] 

* Chain [26]: 1*aux(3)+0
  with precondition: [A=4] 

* Chain [25]: 1*s(11)+0
  Such that:s(11) =< B

  with precondition: [A=4,B>=1] 


#### Cost of chains of l0(A,B,C,D):
* Chain [33]: 1*s(12)+1*s(13)+0
  Such that:s(13) =< A

  with precondition: [0>=C,A>=1] 

* Chain [32]: 0
  with precondition: [A>=1] 

* Chain [31]: 3*s(14)+2*s(16)+0
  Such that:aux(4) =< C
s(14) =< aux(4)

  with precondition: [A>=1,C>=1] 

* Chain [30]...: 1*s(19)+0
  with precondition: [0>=C,A>=1] 

* Chain [29]...: 1*s(20)+1*s(21)+0
  Such that:s(20) =< C

  with precondition: [A>=1,C>=1] 


Closed-form bounds of l0(A,B,C,D): 
-------------------------------------
* Chain [33] with precondition: [0>=C,A>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [32] with precondition: [A>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [31] with precondition: [A>=1,C>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [30]... with precondition: [0>=C,A>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [29]... with precondition: [A>=1,C>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,C,D): inf 
Asymptotic class: infinity 
* Total analysis performed in 82 ms.

