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

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

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

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

### Specialization of cost equations l1/5 
* CE 4 is refined into CE [13] 
* CE 3 is refined into CE [14] 
* CE 2 is refined into CE [15] 


### Cost equations --> "Loop" of l1/5 
* CEs [15] --> Loop 13 
* CEs [13] --> Loop 14 
* CEs [14] --> Loop 15 

### Ranking functions of CR l1(F,X,Y,Z,A1) 
* RF of phase [13]: [X]

#### Partial ranking functions of CR l1(F,X,Y,Z,A1) 
* Partial RF of phase [13]:
  - RF of loop [13:1]:
    X


### Specialization of cost equations l3/7 
* CE 12 is refined into CE [16] 
* CE 11 is refined into CE [17] 
* CE 10 is refined into CE [18] 


### Cost equations --> "Loop" of l3/7 
* CEs [18] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [17] --> Loop 18 

### Ranking functions of CR l3(A,B,F,Y,Z,A1,B1) 

#### Partial ranking functions of CR l3(A,B,F,Y,Z,A1,B1) 


### Specialization of cost equations l2/4 
* CE 7 is refined into CE [19,20,21] 
* CE 9 is refined into CE [22] 
* CE 8 is refined into CE [23,24] 


### Cost equations --> "Loop" of l2/4 
* CEs [24] --> Loop 19 
* CEs [23] --> Loop 20 
* CEs [19,20] --> Loop 21 
* CEs [22] --> Loop 22 
* CEs [21] --> Loop 23 

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

#### Partial ranking functions of CR l2(A,B,F,Y) 
* Partial RF of phase [19,20]:
  - RF of loop [20:1]:
    F depends on loops [19:1] 


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


### Cost equations --> "Loop" of l1_loop_cont/6 
* CEs [28,29] --> Loop 24 
* CEs [25] --> Loop 25 
* CEs [27] --> Loop 26 
* CEs [26] --> Loop 27 

### 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 [30,31,32,33,34,35,36,37] 


### Cost equations --> "Loop" of l0/5 
* CEs [30,31,37] --> Loop 28 
* CEs [34] --> Loop 29 
* CEs [33] --> Loop 30 
* CEs [36] --> Loop 31 
* CEs [32] --> Loop 32 
* CEs [35] --> Loop 33 

### Ranking functions of CR l0(A,B,F,X,Y) 

#### Partial ranking functions of CR l0(A,B,F,X,Y) 


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

#### Cost of chains of l1(F,X,Y,Z,A1):
* Chain [[13],15]: 1*it(13)+0
  Such that:it(13) =< X

  with precondition: [Y=2,A1=0,X>=1] 

* Chain [[13],14]: 1*it(13)+0
  Such that:it(13) =< X

  with precondition: [Y=3,X>=1] 

* Chain [15]: 0
  with precondition: [Y=2,Z=F,X=A1,0>=X] 

* Chain [14]: 0
  with precondition: [Y=3] 


#### Cost of chains of l3(A,B,F,Y,Z,A1,B1):
* Chain [[16]]...: 1*it(16)+0
  with precondition: [F>=B,A>=1,Y>=2,3>=Y] 

* Chain [[16],18]: 1*it(16)+0
  with precondition: [Y=2,F=B1+1,0>=Z,A>=1,F>=B,B>=A1+1,Z>=A1+2] 

* Chain [[16],17]: 1*it(16)+0
  with precondition: [Y=3,A>=1,F>=B] 

* Chain [17]: 0
  with precondition: [Y=3,F>=B] 


#### Cost of chains of l2(A,B,F,Y):
* Chain [[19,20]]...: 4*it(19)+0
  with precondition: [F>=1,Y=3] 

* Chain [[19,20],23]...: 5*it(19)+0
  with precondition: [Y=3,F>=1] 

* Chain [[19,20],22]: 4*it(19)+0
  with precondition: [Y=3,F>=1] 

* Chain [[19,20],21]: 5*aux(1)+0
  with precondition: [Y=3,F>=1] 

* Chain [23]...: 1*s(7)+0
  with precondition: [Y=3,F>=1] 

* Chain [22]: 0
  with precondition: [Y=3] 

* Chain [21]: 1*aux(1)+0
  with precondition: [Y=3,F>=1] 


#### Cost of chains of l1_loop_cont(A,B,C,D,E,F):
* Chain [27]: 0
  with precondition: [A=2] 

* Chain [26]: 1*s(14)+0
  with precondition: [A=2,D>=1] 

* Chain [25]: 0
  with precondition: [A=3] 

* Chain [24]...: 1*aux(4)+0
  with precondition: [A=2,D>=1] 


#### Cost of chains of l0(A,B,F,X,Y):
* Chain [33]...: 1*s(17)+0
  with precondition: [0>=X,F>=1] 

* Chain [32]...: 1*s(18)+1*s(19)+0
  Such that:s(18) =< X

  with precondition: [X>=1] 

* Chain [31]: 0
  with precondition: [] 

* Chain [30]: 0
  with precondition: [0>=X] 

* Chain [29]: 1*s(20)+0
  with precondition: [0>=X,F>=1] 

* Chain [28]: 3*s(21)+1*s(23)+0
  Such that:aux(5) =< X
s(21) =< aux(5)

  with precondition: [X>=1] 


Closed-form bounds of l0(A,B,F,X,Y): 
-------------------------------------
* Chain [33]... with precondition: [0>=X,F>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [32]... with precondition: [X>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [31] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [30] with precondition: [0>=X] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [29] with precondition: [0>=X,F>=1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [28] with precondition: [X>=1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of l0(A,B,F,X,Y): inf 
Asymptotic class: infinity 
* Total analysis performed in 89 ms.

