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

#### Computed strongly connected components 
0. recursive  : [f18/4]
1. non_recursive  : [exit_location/1]
2. recursive  : [f24/4]
3. recursive  : [f31/4]
4. non_recursive  : [f39/7]
5. non_recursive  : [f31_loop_cont/8]
6. non_recursive  : [f24_loop_cont/8]
7. non_recursive  : [f18_loop_cont/8]
8. non_recursive  : [f0/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f18/4
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into f24/4
3. SCC is partially evaluated into f31/4
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into f31_loop_cont/8
6. SCC is partially evaluated into f24_loop_cont/8
7. SCC is partially evaluated into f18_loop_cont/8
8. SCC is partially evaluated into f0/7

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

### Specialization of cost equations f18/4 
* CE 3 is refined into CE [17] 
* CE 4 is refined into CE [18] 
* CE 2 is refined into CE [19] 


### Cost equations --> "Loop" of f18/4 
* CEs [19] --> Loop 17 
* CEs [17] --> Loop 18 
* CEs [18] --> Loop 19 

### Ranking functions of CR f18(A,B,I,J) 
* RF of phase [17]: [-B+10]

#### Partial ranking functions of CR f18(A,B,I,J) 
* Partial RF of phase [17]:
  - RF of loop [17:1]:
    -B+10


### Specialization of cost equations f24/4 
* CE 8 is refined into CE [20] 
* CE 9 is refined into CE [21] 
* CE 7 is refined into CE [22] 


### Cost equations --> "Loop" of f24/4 
* CEs [22] --> Loop 20 
* CEs [20] --> Loop 21 
* CEs [21] --> Loop 22 

### Ranking functions of CR f24(A,B,I,J) 
* RF of phase [20]: [-B+10]

#### Partial ranking functions of CR f24(A,B,I,J) 
* Partial RF of phase [20]:
  - RF of loop [20:1]:
    -B+10


### Specialization of cost equations f31/4 
* CE 14 is refined into CE [23] 
* CE 13 is refined into CE [24] 
* CE 12 is refined into CE [25] 


### Cost equations --> "Loop" of f31/4 
* CEs [25] --> Loop 23 
* CEs [23] --> Loop 24 
* CEs [24] --> Loop 25 

### Ranking functions of CR f31(A,B,I,J) 
* RF of phase [23]: [-B+10]

#### Partial ranking functions of CR f31(A,B,I,J) 
* Partial RF of phase [23]:
  - RF of loop [23:1]:
    -B+10


### Specialization of cost equations f31_loop_cont/8 
* CE 16 is refined into CE [26] 
* CE 15 is refined into CE [27] 


### Cost equations --> "Loop" of f31_loop_cont/8 
* CEs [26] --> Loop 26 
* CEs [27] --> Loop 27 

### Ranking functions of CR f31_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR f31_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations f24_loop_cont/8 
* CE 11 is refined into CE [28,29,30,31] 
* CE 10 is refined into CE [32] 


### Cost equations --> "Loop" of f24_loop_cont/8 
* CEs [29] --> Loop 28 
* CEs [28,31] --> Loop 29 
* CEs [30] --> Loop 30 
* CEs [32] --> Loop 31 

### Ranking functions of CR f24_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR f24_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations f18_loop_cont/8 
* CE 6 is refined into CE [33,34,35,36,37,38] 
* CE 5 is refined into CE [39] 


### Cost equations --> "Loop" of f18_loop_cont/8 
* CEs [37,38] --> Loop 32 
* CEs [34,35,36] --> Loop 33 
* CEs [33] --> Loop 34 
* CEs [39] --> Loop 35 

### Ranking functions of CR f18_loop_cont(A,B,C,D,E,F,G,H) 

#### Partial ranking functions of CR f18_loop_cont(A,B,C,D,E,F,G,H) 


### Specialization of cost equations f0/7 
* CE 1 is refined into CE [40,41,42,43] 


### Cost equations --> "Loop" of f0/7 
* CEs [40,41,42,43] --> Loop 36 

### Ranking functions of CR f0(A,B,C,D,E,F,I) 

#### Partial ranking functions of CR f0(A,B,C,D,E,F,I) 


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

#### Cost of chains of f18(A,B,I,J):
* Chain [[17],19]: 1*it(17)+0
  Such that:it(17) =< -B+10

  with precondition: [A=10,I=3,9>=B,B>=0] 

* Chain [[17],18]: 1*it(17)+0
  Such that:it(17) =< -B+10

  with precondition: [A=10,I=5,J=0,9>=B,B>=0] 

* Chain [19]: 0
  with precondition: [A=10,I=3,B>=0] 


#### Cost of chains of f24(A,B,I,J):
* Chain [[20],22]: 1*it(20)+0
  Such that:it(20) =< -B+10

  with precondition: [A=10,I=3,9>=B] 

* Chain [[20],21]: 1*it(20)+0
  Such that:it(20) =< -B+10

  with precondition: [A=10,I=4,J=0,9>=B] 

* Chain [22]: 0
  with precondition: [A=10,I=3] 

* Chain [21]: 0
  with precondition: [A=10,I=4,J=0,B>=10] 


#### Cost of chains of f31(A,B,I,J):
* Chain [[23],25]: 1*it(23)+0
  Such that:it(23) =< -B+10

  with precondition: [A=10,I=2,J=10,9>=B] 

* Chain [[23],24]: 1*it(23)+0
  Such that:it(23) =< -B+10

  with precondition: [A=10,I=3,9>=B] 

* Chain [25]: 0
  with precondition: [A=10,I=2,B=J,B>=10] 

* Chain [24]: 0
  with precondition: [A=10,I=3] 


#### Cost of chains of f31_loop_cont(A,B,C,D,E,F,G,H):
* Chain [27]: 0
  with precondition: [A=2,B=10,D=10,F=10] 

* Chain [26]: 0
  with precondition: [A=3,B=10,D=10,F=10] 


#### Cost of chains of f24_loop_cont(A,B,C,D,E,F,G,H):
* Chain [31]: 0
  with precondition: [A=3,B=10,D=10,F=10] 

* Chain [30]: 0
  with precondition: [A=4,B=10,D=10,F=10] 

* Chain [29]: 2*s(1)+0
  Such that:aux(1) =< -C+10
s(1) =< aux(1)

  with precondition: [A=4,B=10,D=10,F=10,9>=C] 

* Chain [28]: 0
  with precondition: [A=4,B=10,D=10,F=10,C>=10] 


#### Cost of chains of f18_loop_cont(A,B,C,D,E,F,G,H):
* Chain [35]: 0
  with precondition: [A=3,B=10,D=10,F=10] 

* Chain [34]: 0
  with precondition: [A=5,B=10,D=10,F=10] 

* Chain [33]: 3*s(3)+2*s(7)+0
  Such that:s(6) =< 10
aux(2) =< -C+10
s(3) =< aux(2)
s(7) =< s(6)

  with precondition: [A=5,B=10,D=10,F=10,9>=C] 

* Chain [32]: 20
  with precondition: [A=5,B=10,D=10,F=10,C>=10] 


#### Cost of chains of f0(A,B,C,D,E,F,I):
* Chain [36]: 80
  with precondition: [] 


Closed-form bounds of f0(A,B,C,D,E,F,I): 
-------------------------------------
* Chain [36] with precondition: [] 
    - Upper bound: 80 
    - Complexity: constant 

### Maximum cost of f0(A,B,C,D,E,F,I): 80 
Asymptotic class: constant 
* Total analysis performed in 97 ms.

