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

#### Computed strongly connected components 
0. recursive  : [f6/8]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f14/5]
3. non_recursive  : [f6_loop_cont/6]
4. non_recursive  : [f0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f6/8
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f6_loop_cont/6
4. SCC is partially evaluated into f0/5

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

### Specialization of cost equations f6/8 
* CE 7 is refined into CE [10] 
* CE 5 is refined into CE [11] 
* CE 4 is refined into CE [12] 
* CE 6 is refined into CE [13] 
* CE 3 is refined into CE [14] 
* CE 2 is refined into CE [15] 


### Cost equations --> "Loop" of f6/8 
* CEs [14] --> Loop 10 
* CEs [15] --> Loop 11 
* CEs [10] --> Loop 12 
* CEs [11] --> Loop 13 
* CEs [12] --> Loop 14 
* CEs [13] --> Loop 15 

### Ranking functions of CR f6(A,B,C,D,E,F,G,H) 
* RF of phase [10]: [A,B+C-D]

#### Partial ranking functions of CR f6(A,B,C,D,E,F,G,H) 
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    A
    B+C-D


### Specialization of cost equations f6_loop_cont/6 
* CE 9 is refined into CE [16] 
* CE 8 is refined into CE [17] 


### Cost equations --> "Loop" of f6_loop_cont/6 
* CEs [16] --> Loop 16 
* CEs [17] --> Loop 17 

### Ranking functions of CR f6_loop_cont(A,B,C,D,E,F) 

#### Partial ranking functions of CR f6_loop_cont(A,B,C,D,E,F) 


### Specialization of cost equations f0/5 
* CE 1 is refined into CE [18,19,20,21,22,23,24,25,26,27,28] 


### Cost equations --> "Loop" of f0/5 
* CEs [27,28] --> Loop 18 
* CEs [23] --> Loop 19 
* CEs [22] --> Loop 20 
* CEs [26] --> Loop 21 
* CEs [25] --> Loop 22 
* CEs [21] --> Loop 23 
* CEs [19] --> Loop 24 
* CEs [20] --> Loop 25 
* CEs [18] --> Loop 26 
* CEs [24] --> Loop 27 

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

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


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

#### Cost of chains of f6(A,B,C,D,E,F,G,H):
* Chain [[11]]...: 1*it(11)+0
  with precondition: [0>=A+1,B>=A,A+D=B+C] 

* Chain [[11],12]: 1*it(11)+0
  with precondition: [E=3,A+D=B+C,0>=A+1,B>=A] 

* Chain [[10],15]: 1*it(10)+0
  Such that:it(10) =< A

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

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

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

* Chain [[10],13]: 1*it(10)+0
  Such that:it(10) =< A

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

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

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

* Chain [15]: 0
  with precondition: [A=0,C=0,E=2,F=0,G=0,D=B,D=H,D>=0] 

* Chain [14]: 0
  with precondition: [A=0,E=2,F=0,D=H,D=B+C,D=B+G,B>=0,D>=B+1] 

* Chain [13]: 0
  with precondition: [A=0,E=2,F=0,D=H,D=B+C,D=B+G,B>=0,B>=D+1] 

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


#### Cost of chains of f6_loop_cont(A,B,C,D,E,F):
* Chain [17]: 0
  with precondition: [A=2] 

* Chain [16]: 0
  with precondition: [A=3] 


#### Cost of chains of f0(A,B,C,D,E):
* Chain [27]: 0
  with precondition: [] 

* Chain [26]: 0
  with precondition: [B=0,D=0] 

* Chain [25]: 0
  with precondition: [B=0,0>=D+1] 

* Chain [24]: 0
  with precondition: [B=0,D>=1] 

* Chain [23]: 1*s(1)+0
  Such that:s(1) =< B

  with precondition: [B=D,B>=1] 

* Chain [22]: 1*s(2)+0
  with precondition: [0>=B+1] 

* Chain [21]: 1*s(3)+0
  Such that:s(3) =< B

  with precondition: [B>=1] 

* Chain [20]: 1*s(4)+0
  Such that:s(4) =< B

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

* Chain [19]: 1*s(5)+0
  Such that:s(5) =< B

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

* Chain [18]...: 1*aux(1)+0
  with precondition: [0>=B+1] 


Closed-form bounds of f0(A,B,C,D,E): 
-------------------------------------
* Chain [27] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [26] with precondition: [B=0,D=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [25] with precondition: [B=0,0>=D+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [24] with precondition: [B=0,D>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [23] with precondition: [B=D,B>=1] 
    - Upper bound: B 
    - Complexity: n 
* Chain [22] with precondition: [0>=B+1] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [21] with precondition: [B>=1] 
    - Upper bound: B 
    - Complexity: n 
* Chain [20] with precondition: [B>=1,D>=B+1] 
    - Upper bound: B 
    - Complexity: n 
* Chain [19] with precondition: [B>=1,B>=D+1] 
    - Upper bound: B 
    - Complexity: n 
* Chain [18]... with precondition: [0>=B+1] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f0(A,B,C,D,E): inf 
Asymptotic class: infinity 
* Total analysis performed in 113 ms.

