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

#### Computed strongly connected components 
0. recursive  : [f2/4]
1. recursive  : [f2_loop_cont/7,f300/6]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f1/4]
4. non_recursive  : [f300_loop_cont/5]
5. non_recursive  : [f3/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/4
1. SCC is partially evaluated into f300/6
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into f300_loop_cont/5
5. SCC is partially evaluated into f3/4

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

### Specialization of cost equations f2/4 
* CE 10 is refined into CE [11] 
* CE 9 is refined into CE [12] 
* CE 8 is refined into CE [13] 


### Cost equations --> "Loop" of f2/4 
* CEs [13] --> Loop 11 
* CEs [11] --> Loop 12 
* CEs [12] --> Loop 13 

### Ranking functions of CR f2(A,B,E,F) 

#### Partial ranking functions of CR f2(A,B,E,F) 


### Specialization of cost equations f300/6 
* CE 4 is refined into CE [14] 
* CE 2 is refined into CE [15,16,17] 
* CE 5 is refined into CE [18] 
* CE 3 is refined into CE [19,20] 


### Cost equations --> "Loop" of f300/6 
* CEs [20] --> Loop 14 
* CEs [19] --> Loop 15 
* CEs [14] --> Loop 16 
* CEs [16] --> Loop 17 
* CEs [15] --> Loop 18 
* CEs [18] --> Loop 19 
* CEs [17] --> Loop 20 

### Ranking functions of CR f300(A,B,C,E,F,G) 

#### Partial ranking functions of CR f300(A,B,C,E,F,G) 


### Specialization of cost equations f300_loop_cont/5 
* CE 6 is refined into CE [21] 
* CE 7 is refined into CE [22] 


### Cost equations --> "Loop" of f300_loop_cont/5 
* CEs [21] --> Loop 21 
* CEs [22] --> Loop 22 

### Ranking functions of CR f300_loop_cont(A,B,C,D,E) 

#### Partial ranking functions of CR f300_loop_cont(A,B,C,D,E) 


### Specialization of cost equations f3/4 
* CE 1 is refined into CE [23,24,25,26,27,28,29,30,31,32,33] 


### Cost equations --> "Loop" of f3/4 
* CEs [32,33] --> Loop 23 
* CEs [29,30,31] --> Loop 24 
* CEs [27] --> Loop 25 
* CEs [26] --> Loop 26 
* CEs [25] --> Loop 27 
* CEs [24,28] --> Loop 28 
* CEs [23] --> Loop 29 

### Ranking functions of CR f3(A,B,C,E) 

#### Partial ranking functions of CR f3(A,B,C,E) 


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

#### Cost of chains of f2(A,B,E,F):
* Chain [[11]]...: 1*it(11)+0
  with precondition: [29>=A,19>=B,E>=2,3>=E] 

* Chain [[11],12]: 1*it(11)+0
  with precondition: [E=3,29>=A,19>=B] 

* Chain [13]: 0
  with precondition: [E=2,B=F+1,19>=B,A>=30] 

* Chain [12]: 0
  with precondition: [E=3,19>=B] 


#### Cost of chains of f300(A,B,C,E,F,G):
* Chain [[15]]...: 1*it(15)+0
  with precondition: [A>=30,19>=B] 

* Chain [[15],19]: 1*it(15)+0
  with precondition: [E=3,19>=B,A>=30] 

* Chain [[15],17]: 1*it(15)+0
  with precondition: [E=3,19>=B,A>=30] 

* Chain [[14]]...: 2*it(14)+0
  with precondition: [29>=A,19>=B] 

* Chain [[14],20]...: 3*it(14)+0
  with precondition: [E=3,29>=A,19>=B] 

* Chain [[14],19]: 2*it(14)+0
  with precondition: [E=3,29>=A,19>=B] 

* Chain [[14],18]: 3*it(14)+0
  with precondition: [E=3,29>=A,19>=B] 

* Chain [[14],17]: 2*it(14)+0
  with precondition: [E=3,29>=A,19>=B] 

* Chain [[14],16]: 2*it(14)+0
  with precondition: [E=4,29>=A,19>=B,F>=20] 

* Chain [20]...: 1*s(4)+0
  with precondition: [E=3,29>=A,19>=B] 

* Chain [19]: 0
  with precondition: [E=3] 

* Chain [18]: 1*s(5)+0
  with precondition: [E=3,29>=A,19>=B] 

* Chain [17]: 0
  with precondition: [E=3,19>=B] 

* Chain [16]: 0
  with precondition: [E=4,B=F,B>=20] 


#### Cost of chains of f300_loop_cont(A,B,C,D,E):
* Chain [22]: 0
  with precondition: [A=3] 

* Chain [21]: 0
  with precondition: [A=4] 


#### Cost of chains of f3(A,B,C,E):
* Chain [29]: 0
  with precondition: [] 

* Chain [28]: 1*aux(4)+0
  with precondition: [29>=A,19>=B] 

* Chain [27]: 0
  with precondition: [19>=B] 

* Chain [26]: 1*s(16)+0
  with precondition: [19>=B,A>=30] 

* Chain [25]: 0
  with precondition: [B>=20] 

* Chain [24]...: 1*aux(5)+0
  with precondition: [29>=A,19>=B] 

* Chain [23]...: 1*aux(6)+0
  with precondition: [19>=B,A>=30] 


Closed-form bounds of f3(A,B,C,E): 
-------------------------------------
* Chain [29] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [28] with precondition: [29>=A,19>=B] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [27] with precondition: [19>=B] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [26] with precondition: [19>=B,A>=30] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [25] with precondition: [B>=20] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [24]... with precondition: [29>=A,19>=B] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [23]... with precondition: [19>=B,A>=30] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f3(A,B,C,E): inf 
Asymptotic class: infinity 
* Total analysis performed in 80 ms.

