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

#### Computed strongly connected components 
0. recursive  : [f0/5]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f0_loop_cont/2]
3. non_recursive  : [f3/7]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f0/5
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f3/7

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

### Specialization of cost equations f0/5 
* CE 4 is refined into CE [5] 
* CE 2 is refined into CE [6] 
* CE 3 is refined into CE [7] 


### Cost equations --> "Loop" of f0/5 
* CEs [6] --> Loop 5 
* CEs [7] --> Loop 6 
* CEs [5] --> Loop 7 

### Ranking functions of CR f0(A,B,C,D,H) 
* RF of phase [5,6]: [-A/5000+5001/5000*C+4999]

#### Partial ranking functions of CR f0(A,B,C,D,H) 
* Partial RF of phase [5,6]:
  - RF of loop [5:1]:
    A depends on loops [6:1] 
    C+4999
  - RF of loop [6:1]:
    -A/5000+1/5000 depends on loops [5:1] 


### Specialization of cost equations f3/7 
* CE 1 is refined into CE [8,9] 


### Cost equations --> "Loop" of f3/7 
* CEs [8,9] --> Loop 8 

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

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


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

#### Cost of chains of f0(A,B,C,D,H):
* Chain [[5,6],7]: 1*it(5)+1*it(6)+0
  Such that:aux(6) =< -A/5000+5001/5000*C+4999
aux(7) =< -A/5000+5001/5000*C+24999999/5000
it(5) =< C+4999
it(5) =< aux(6)
it(6) =< aux(6)
it(5) =< aux(7)
it(6) =< aux(7)

  with precondition: [H=2,5000>=A,C+4998>=0,C+4999>=A] 

* Chain [7]: 0
  with precondition: [H=2,5000>=A,C+4999>=A] 


#### Cost of chains of f3(A,B,C,D,E,F,H):
* Chain [8]: 1*aux(8)+0
  with precondition: [] 


Closed-form bounds of f3(A,B,C,D,E,F,H): 
-------------------------------------
* Chain [8] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f3(A,B,C,D,E,F,H): inf 
Asymptotic class: infinity 
* Total analysis performed in 35 ms.

