/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  : [f1/5]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f1_loop_cont/2]
3. non_recursive  : [f0/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/5
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f0/5

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

### Specialization of cost equations f1/5 
* 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 f1/5 
* CEs [6] --> Loop 5 
* CEs [7] --> Loop 6 
* CEs [5] --> Loop 7 

### Ranking functions of CR f1(A,B,C,D,E) 
* RF of phase [5]: [-A/2+B-3/2,B-1]
* RF of phase [6]: [A/2-B+1,-B+3]

#### Partial ranking functions of CR f1(A,B,C,D,E) 
* Partial RF of phase [5]:
  - RF of loop [5:1]:
    -A/2+B-3/2
    B-1
* Partial RF of phase [6]:
  - RF of loop [6:1]:
    A/2-B+1
    -B+3


### Specialization of cost equations f0/5 
* CE 1 is refined into CE [8,9,10] 


### Cost equations --> "Loop" of f0/5 
* CEs [10] --> Loop 8 
* CEs [9] --> Loop 9 
* CEs [8] --> Loop 10 

### Ranking functions of CR f0(A,B,C,D,E) 

#### Partial ranking functions of CR f0(A,B,C,D,E) 


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

#### Cost of chains of f1(A,B,C,D,E):
* Chain [[6],7]: 1*it(6)+0
  Such that:it(6) =< A/2-B+1

  with precondition: [C=2,E=2,3>=A,A>=0,B>=0,A+1>=2*B] 

* Chain [[5],7]: 1*it(5)+0
  Such that:it(5) =< -A/2+B

  with precondition: [C=2,E=2,3>=B,A>=0,2*B>=A+4] 

* Chain [7]: 0
  with precondition: [C=2,E=2,3>=A,3>=B,A>=0,B>=0] 


#### Cost of chains of f0(A,B,C,D,E):
* Chain [10]: 0
  with precondition: [3>=A,3>=B,A>=0,B>=0] 

* Chain [9]: 1*s(1)+0
  Such that:s(1) =< A/2-B+1

  with precondition: [3>=A,A>=0,B>=0,A+1>=2*B] 

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

  with precondition: [3>=B,A>=0,2*B>=A+4] 


Closed-form bounds of f0(A,B,C,D,E): 
-------------------------------------
* Chain [10] with precondition: [3>=A,3>=B,A>=0,B>=0] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [9] with precondition: [3>=A,A>=0,B>=0,A+1>=2*B] 
    - Upper bound: A/2-B+1 
    - Complexity: n 
* Chain [8] with precondition: [3>=B,A>=0,2*B>=A+4] 
    - Upper bound: -A/2+B 
    - Complexity: n 

### Maximum cost of f0(A,B,C,D,E): max([nat(A/2-B+1),nat(-A/2+B)]) 
Asymptotic class: n 
* Total analysis performed in 107 ms.