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

#### Computed strongly connected components 
0. recursive  : [evalfbb1in/5,evalfbb2in/5,evalfbb3in/5,evalfbbin/5]
1. non_recursive  : [evalfstop/4]
2. non_recursive  : [evalfreturnin/4]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [evalfbb3in_loop_cont/5]
5. non_recursive  : [evalfentryin/4]
6. non_recursive  : [evalfstart/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into evalfbb3in/5
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into evalfbb3in_loop_cont/5
5. SCC is partially evaluated into evalfentryin/4
6. SCC is partially evaluated into evalfstart/4

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

### Specialization of cost equations evalfbb3in/5 
* CE 7 is refined into CE [10] 
* CE 6 is refined into CE [11] 
* CE 5 is refined into CE [12] 
* CE 4 is refined into CE [13] 
* CE 3 is refined into CE [14] 


### Cost equations --> "Loop" of evalfbb3in/5 
* CEs [13] --> Loop 10 
* CEs [14] --> Loop 11 
* CEs [10] --> Loop 12 
* CEs [11] --> Loop 13 
* CEs [12] --> Loop 14 

### Ranking functions of CR evalfbb3in(A,B,C,D,E) 
* RF of phase [10]: [C]
* RF of phase [11]: [B-C]

#### Partial ranking functions of CR evalfbb3in(A,B,C,D,E) 
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    C
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    B-C


### Specialization of cost equations evalfbb3in_loop_cont/5 
* CE 9 is refined into CE [15] 
* CE 8 is refined into CE [16] 


### Cost equations --> "Loop" of evalfbb3in_loop_cont/5 
* CEs [15] --> Loop 15 
* CEs [16] --> Loop 16 

### Ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR evalfbb3in_loop_cont(A,B,C,D,E) 


### Specialization of cost equations evalfentryin/4 
* CE 2 is refined into CE [17,18,19,20,21] 


### Cost equations --> "Loop" of evalfentryin/4 
* CEs [21] --> Loop 17 
* CEs [18,20] --> Loop 18 
* CEs [17,19] --> Loop 19 

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

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


### Specialization of cost equations evalfstart/4 
* CE 1 is refined into CE [22,23,24] 


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

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

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


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

#### Cost of chains of evalfbb3in(A,B,C,D,E):
* Chain [[11],13]: 1*it(11)+0
  Such that:it(11) =< -C+E

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

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

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

* Chain [[10],14]: 1*it(10)+0
  Such that:it(10) =< C

  with precondition: [D=2,E=0,0>=A,C>=1,B>=C+1] 

* Chain [[10],12]: 1*it(10)+0
  Such that:it(10) =< C

  with precondition: [D=3,0>=A,C>=1,B>=C+1] 

* Chain [12]: 0
  with precondition: [D=3,B>=2,C>=0,B>=C] 


#### Cost of chains of evalfbb3in_loop_cont(A,B,C,D,E):
* Chain [16]: 0
  with precondition: [A=2,C>=2] 

* Chain [15]: 0
  with precondition: [A=3,C>=2] 


#### Cost of chains of evalfentryin(A,B,C,D):
* Chain [19]: 2*s(1)+0
  Such that:aux(1) =< A
s(1) =< aux(1)

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

* Chain [18]: 2*s(3)+0
  Such that:aux(2) =< -A+B
s(3) =< aux(2)

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

* Chain [17]: 0
  with precondition: [A>=1,B>=A+1] 


#### Cost of chains of evalfstart(A,B,C,D):
* Chain [22]: 2*s(6)+0
  Such that:s(5) =< A
s(6) =< s(5)

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

* Chain [21]: 2*s(8)+0
  Such that:s(7) =< -A+B
s(8) =< s(7)

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

* Chain [20]: 0
  with precondition: [A>=1,B>=A+1] 


Closed-form bounds of evalfstart(A,B,C,D): 
-------------------------------------
* Chain [22] with precondition: [0>=C,A>=1,B>=A+1] 
    - Upper bound: 2*A 
    - Complexity: n 
* Chain [21] with precondition: [A>=1,C>=1,B>=A+1] 
    - Upper bound: -2*A+2*B 
    - Complexity: n 
* Chain [20] with precondition: [A>=1,B>=A+1] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of evalfstart(A,B,C,D): max([-2*A+2*B,2*A]) 
Asymptotic class: n 
* Total analysis performed in 69 ms.

