WARNING: Excluded non-linear constraints:[I=3*A+2*B+C*C]
WARNING: Excluded non-linear constraints:[I=3*A+2*B+C*C]

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

#### Computed strongly connected components 
0. recursive  : [l1/8]
1. non_recursive  : [exit_location/1]
2. recursive  : [l2/2]
3. non_recursive  : [l2_loop_cont/2]
4. non_recursive  : [l1_loop_cont/6]
5. non_recursive  : [l0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into l1/8
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into l2/2
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into l1_loop_cont/6
5. SCC is partially evaluated into l0/5

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

### Specialization of cost equations l1/8 
* CE 4 is refined into CE [10] 
* CE 5 is refined into CE [11] 
* CE 3 is refined into CE [12] 
* CE 2 is refined into CE [13] 


### Cost equations --> "Loop" of l1/8 
* CEs [12] --> Loop 10 
* CEs [13] --> Loop 11 
* CEs [10] --> Loop 12 
* CEs [11] --> Loop 13 

### Ranking functions of CR l1(X1,X2,X3,X4,Y4,Z4,A5,B5) 
* RF of phase [10,11]: [X4]

#### Partial ranking functions of CR l1(X1,X2,X3,X4,Y4,Z4,A5,B5) 
* Partial RF of phase [10,11]:
  - RF of loop [10:1]:
    X4/2
  - RF of loop [11:1]:
    X4


### Specialization of cost equations l2/2 
* CE 9 is refined into CE [14] 
* CE 8 is refined into CE [15] 


### Cost equations --> "Loop" of l2/2 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR l2(X4,Y4) 
* RF of phase [14]: [X4]

#### Partial ranking functions of CR l2(X4,Y4) 
* Partial RF of phase [14]:
  - RF of loop [14:1]:
    X4


### Specialization of cost equations l1_loop_cont/6 
* CE 7 is refined into CE [16,17] 
* CE 6 is refined into CE [18] 


### Cost equations --> "Loop" of l1_loop_cont/6 
* CEs [17] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [18] --> Loop 18 

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

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


### Specialization of cost equations l0/5 
* CE 1 is refined into CE [19,20,21,22,23,24] 


### Cost equations --> "Loop" of l0/5 
* CEs [20,23,24] --> Loop 19 
* CEs [22] --> Loop 20 
* CEs [21] --> Loop 21 
* CEs [19] --> Loop 22 

### Ranking functions of CR l0(X1,X2,X3,X4,Y4) 

#### Partial ranking functions of CR l0(X1,X2,X3,X4,Y4) 


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

#### Cost of chains of l1(X1,X2,X3,X4,Y4,Z4,A5,B5):
* Chain [[10,11],13]: 1*it(10)+1*it(11)+0
  Such that:aux(1) =< X4
aux(2) =< X4+1
it(10) =< X4/2
it(10) =< aux(1)
it(11) =< aux(1)
it(10) =< aux(2)
it(11) =< aux(2)

  with precondition: [Y4=2,X4>=1] 

* Chain [[10,11],12]: 1*it(10)+1*it(11)+0
  Such that:aux(1) =< X4
aux(2) =< X4+1
it(10) =< X4/2
it(10) =< aux(1)
it(11) =< aux(1)
it(10) =< aux(2)
it(11) =< aux(2)

  with precondition: [Y4=3,Z4=B5,X4>=1] 

* Chain [13]: 0
  with precondition: [Y4=2] 

* Chain [12]: 0
  with precondition: [Y4=3,A5=X2,X1=Z4,X1=B5,0>=X4] 


#### Cost of chains of l2(X4,Y4):
* Chain [[14],15]: 1*it(14)+0
  Such that:it(14) =< X4

  with precondition: [Y4=2,X4>=1] 

* Chain [15]: 0
  with precondition: [Y4=2] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F):
* Chain [18]: 0
  with precondition: [A=2] 

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

* Chain [16]: 1*s(1)+0
  Such that:s(1) =< E

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


#### Cost of chains of l0(X1,X2,X3,X4,Y4):
* Chain [22]: 0
  with precondition: [] 

* Chain [21]: 0
  with precondition: [0>=X4] 

* Chain [20]: 1*s(2)+0
  Such that:s(2) =< X1

  with precondition: [0>=X4,X1>=1] 

* Chain [19]: 3*s(5)+3*s(6)+1*s(15)+0
  Such that:aux(3) =< X4
aux(4) =< X4+1
aux(5) =< X4/2
s(5) =< aux(5)
s(5) =< aux(3)
s(6) =< aux(3)
s(5) =< aux(4)
s(6) =< aux(4)

  with precondition: [X4>=1] 


Closed-form bounds of l0(X1,X2,X3,X4,Y4): 
-------------------------------------
* Chain [22] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [21] with precondition: [0>=X4] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [20] with precondition: [0>=X4,X1>=1] 
    - Upper bound: X1 
    - Complexity: n 
* Chain [19] with precondition: [X4>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(X1,X2,X3,X4,Y4): inf 
Asymptotic class: infinity 
* Total analysis performed in 82 ms.

