/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^2))  

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

#### Computed strongly connected components 
0. recursive  : [f3/3]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f3_loop_cont/2]
3. non_recursive  : [f1/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f3/3
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f1/3

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

### Specialization of cost equations f3/3 
* CE 4 is refined into CE [5] 
* CE 3 is refined into CE [6] 
* CE 2 is refined into CE [7] 


### Cost equations --> "Loop" of f3/3 
* CEs [6] --> Loop 5 
* CEs [7] --> Loop 6 
* CEs [5] --> Loop 7 

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

#### Partial ranking functions of CR f3(A,B,C) 
* Partial RF of phase [5,6]:
  - RF of loop [5:1]:
    A-1
    -B+1 depends on loops [6:1] 
  - RF of loop [6:1]:
    B depends on loops [5:1] 


### Specialization of cost equations f1/3 
* CE 1 is refined into CE [8] 


### Cost equations --> "Loop" of f1/3 
* CEs [8] --> Loop 8 

### Ranking functions of CR f1(A,B,C) 

#### Partial ranking functions of CR f1(A,B,C) 


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

#### Cost of chains of f3(A,B,C):
* Chain [[5,6],7]: 1*it(5)+1*it(6)+0
  Such that:aux(4) =< B
aux(9) =< A
it(5) =< aux(9)
aux(3) =< it(5)*aux(9)
it(6) =< aux(3)+aux(4)

  with precondition: [C=2,A>=1,A>=B] 

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


#### Cost of chains of f1(A,B,C):
* Chain [8]: 1*s(8)+1*s(10)+0
  Such that:aux(10) =< A
s(8) =< aux(10)
s(9) =< s(8)*aux(10)
s(10) =< s(9)+aux(10)

  with precondition: [A>=1] 


Closed-form bounds of f1(A,B,C): 
-------------------------------------
* Chain [8] with precondition: [A>=1] 
    - Upper bound: 2*A+A*A 
    - Complexity: n^2 

### Maximum cost of f1(A,B,C): 2*A+A*A 
Asymptotic class: n^2 
* Total analysis performed in 64 ms.