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

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

#### Computed strongly connected components 
0. recursive  : [l1/6]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [l1a/4]
3. recursive  : [l2/2]
4. non_recursive  : [l2_loop_cont/2]
5. non_recursive  : [l1_loop_cont/5]
6. non_recursive  : [l0/4]

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

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

### Specialization of cost equations l1/6 
* CE 4 is refined into CE [11] 
* CE 2 is refined into CE [12] 
* CE 5 is refined into CE [13] 
* CE 3 is refined into CE [14] 


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

### Ranking functions of CR l1(X1,X2,X3,Y3,Z3,A4) 
* RF of phase [11]: [X1]

#### Partial ranking functions of CR l1(X1,X2,X3,Y3,Z3,A4) 
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    X1


### Specialization of cost equations l2/2 
* CE 10 is refined into CE [15] 
* CE 9 is refined into CE [16] 


### Cost equations --> "Loop" of l2/2 
* CEs [16] --> Loop 15 
* CEs [15] --> Loop 16 

### Ranking functions of CR l2(X3,Y3) 
* RF of phase [15]: [X3]

#### Partial ranking functions of CR l2(X3,Y3) 
* Partial RF of phase [15]:
  - RF of loop [15:1]:
    X3


### Specialization of cost equations l1_loop_cont/5 
* CE 8 is refined into CE [17,18] 
* CE 6 is refined into CE [19] 
* CE 7 is refined into CE [20] 


### Cost equations --> "Loop" of l1_loop_cont/5 
* CEs [18] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [19] --> Loop 19 
* CEs [20] --> Loop 20 

### 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 [21,22,23,24,25,26,27,28] 


### Cost equations --> "Loop" of l0/4 
* CEs [26] --> Loop 21 
* CEs [24] --> Loop 22 
* CEs [22,23,27,28] --> Loop 23 
* CEs [21,25] --> Loop 24 

### Ranking functions of CR l0(X1,X2,X3,Y3) 

#### Partial ranking functions of CR l0(X1,X2,X3,Y3) 


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

#### Cost of chains of l1(X1,X2,X3,Y3,Z3,A4):
* Chain [[11],14]: 1*it(11)+0
  Such that:it(11) =< X1

  with precondition: [Y3=2,X1>=1] 

* Chain [[11],13]: 1*it(11)+0
  Such that:it(11) =< X1-Z3

  with precondition: [Y3=3,Z3>=0,X1>=Z3+2] 

* Chain [[11],12]: 1*it(11)+0
  Such that:it(11) =< X1-Z3

  with precondition: [Y3=4,Z3>=0,X1>=Z3+1] 

* Chain [14]: 0
  with precondition: [Y3=2] 

* Chain [13]: 0
  with precondition: [Y3=3,A4=X3,X1=Z3+1,X1>=1] 

* Chain [12]: 0
  with precondition: [Y3=4,Z3=X1,A4=X3] 


#### Cost of chains of l2(X3,Y3):
* Chain [[15],16]: 1*it(15)+0
  Such that:it(15) =< X3

  with precondition: [Y3=2,X3>=1] 

* Chain [16]: 0
  with precondition: [Y3=2] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E):
* Chain [20]: 0
  with precondition: [A=2] 

* Chain [19]: 0
  with precondition: [A=3] 

* Chain [18]: 0
  with precondition: [A=4] 

* Chain [17]: 1*s(1)+0
  Such that:s(1) =< D

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


#### Cost of chains of l0(X1,X2,X3,Y3):
* Chain [24]: 0
  with precondition: [] 

* Chain [23]: 3*s(2)+1*s(5)+0
  Such that:aux(1) =< X1
s(2) =< aux(1)

  with precondition: [X1>=1] 

* Chain [22]: 1*s(6)+0
  Such that:s(6) =< X1

  with precondition: [X1>=2] 

* Chain [21]: 1*s(7)+0
  Such that:s(7) =< X3

  with precondition: [X3>=1] 


Closed-form bounds of l0(X1,X2,X3,Y3): 
-------------------------------------
* Chain [24] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [23] with precondition: [X1>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [22] with precondition: [X1>=2] 
    - Upper bound: X1 
    - Complexity: n 
* Chain [21] with precondition: [X3>=1] 
    - Upper bound: X3 
    - Complexity: n 

### Maximum cost of l0(X1,X2,X3,Y3): inf 
Asymptotic class: infinity 
* Total analysis performed in 47 ms.

