/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [f2/3]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f2_loop_cont/2]
3. non_recursive  : [f1/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f2/3
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 f2/3 
* 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 f2/3 
* CEs [6] --> Loop 5 
* CEs [7] --> Loop 6 
* CEs [5] --> Loop 7 

### Ranking functions of CR f2(A,B,C) 
* RF of phase [5,6]: [A+B-2]

#### Partial ranking functions of CR f2(A,B,C) 
* Partial RF of phase [5,6]:
  - RF of loop [5:1]:
    A-1
  - RF of loop [6:1]:
    B-1


### Specialization of cost equations f1/3 
* CE 1 is refined into CE [8,9] 


### Cost equations --> "Loop" of f1/3 
* CEs [9] --> Loop 8 
* CEs [8] --> Loop 9 

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

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


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

#### Cost of chains of f2(A,B,C):
* Chain [[5,6],7]: 1*it(5)+1*it(6)+0
  Such that:it(5) =< A
it(6) =< B
aux(3) =< A+B
it(5) =< aux(3)
it(6) =< aux(3)

  with precondition: [C=2,A>=1,B>=1,A+B>=3] 

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


#### Cost of chains of f1(A,B,C):
* Chain [9]: 0
  with precondition: [A>=1,B>=1] 

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

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


Closed-form bounds of f1(A,B,C): 
-------------------------------------
* Chain [9] with precondition: [A>=1,B>=1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [8] with precondition: [A>=1,B>=1,A+B>=3] 
    - Upper bound: A+B 
    - Complexity: n 

### Maximum cost of f1(A,B,C): A+B 
Asymptotic class: n 
* Total analysis performed in 59 ms.