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

#### Computed strongly connected components 
0. recursive  : [a/2]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [a_loop_cont/2]
3. non_recursive  : [start/2]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into a/2
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into start/2

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

### Specialization of cost equations a/2 
* 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 a/2 
* CEs [6] --> Loop 5 
* CEs [7] --> Loop 6 
* CEs [5] --> Loop 7 

### Ranking functions of CR a(A,C) 
* RF of phase [5,6]: [A-1]

#### Partial ranking functions of CR a(A,C) 
* Partial RF of phase [5,6]:
  - RF of loop [5:1]:
    A-1
  - RF of loop [6:1]:
    2/3*A-1


### Specialization of cost equations start/2 
* CE 1 is refined into CE [8,9] 


### Cost equations --> "Loop" of start/2 
* CEs [8] --> Loop 8 
* CEs [9] --> Loop 9 

### Ranking functions of CR start(A,C) 

#### Partial ranking functions of CR start(A,C) 


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

#### Cost of chains of a(A,C):
* Chain [[5,6],7]: 1*it(5)+1*it(6)+0
  Such that:it(6) =< 2/3*A
aux(3) =< A
it(5) =< aux(3)
it(6) =< aux(3)

  with precondition: [C=2,A>=2] 

* Chain [7]: 0
  with precondition: [C=2,2*A>=1] 


#### Cost of chains of start(A,C):
* Chain [9]: 0
  with precondition: [A>=1] 

* Chain [8]: 1*s(1)+1*s(3)+0
  Such that:s(2) =< A
s(1) =< 2/3*A
s(3) =< s(2)
s(1) =< s(2)

  with precondition: [A>=2] 


Closed-form bounds of start(A,C): 
-------------------------------------
* Chain [9] with precondition: [A>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [8] with precondition: [A>=2] 
    - Upper bound: 5/3*A 
    - Complexity: n 

### Maximum cost of start(A,C): 5/3*A 
Asymptotic class: n 
* Total analysis performed in 21 ms.

