/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^1))  

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

#### Computed strongly connected components 
0. recursive  : [f300/5]
1. non_recursive  : [exit_location/1]
2. non_recursive  : [f1/3]
3. non_recursive  : [f300_loop_cont/4]
4. non_recursive  : [f2/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f300/5
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f300_loop_cont/4
4. SCC is partially evaluated into f2/3

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

### Specialization of cost equations f300/5 
* CE 4 is refined into CE [7] 
* CE 2 is refined into CE [8] 
* CE 3 is refined into CE [9] 


### Cost equations --> "Loop" of f300/5 
* CEs [9] --> Loop 7 
* CEs [7] --> Loop 8 
* CEs [8] --> Loop 9 

### Ranking functions of CR f300(A,B,D,E,F) 
* RF of phase [7]: [A+1]

#### Partial ranking functions of CR f300(A,B,D,E,F) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    A+1


### Specialization of cost equations f300_loop_cont/4 
* CE 6 is refined into CE [10] 
* CE 5 is refined into CE [11] 


### Cost equations --> "Loop" of f300_loop_cont/4 
* CEs [10] --> Loop 10 
* CEs [11] --> Loop 11 

### Ranking functions of CR f300_loop_cont(A,B,C,D) 

#### Partial ranking functions of CR f300_loop_cont(A,B,C,D) 


### Specialization of cost equations f2/3 
* CE 1 is refined into CE [12,13,14,15] 


### Cost equations --> "Loop" of f2/3 
* CEs [12,15] --> Loop 12 
* CEs [13] --> Loop 13 
* CEs [14] --> Loop 14 

### Ranking functions of CR f2(A,B,D) 

#### Partial ranking functions of CR f2(A,B,D) 


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

#### Cost of chains of f300(A,B,D,E,F):
* Chain [[7],9]: 1*it(7)+0
  Such that:it(7) =< A+1

  with precondition: [D=2,E+1=0,A>=0] 

* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< A+1

  with precondition: [D=3,A>=0] 

* Chain [9]: 0
  with precondition: [D=2,A=E,0>=A+1] 

* Chain [8]: 0
  with precondition: [D=3] 


#### Cost of chains of f300_loop_cont(A,B,C,D):
* Chain [11]: 0
  with precondition: [A=2] 

* Chain [10]: 0
  with precondition: [A=3] 


#### Cost of chains of f2(A,B,D):
* Chain [14]: 0
  with precondition: [] 

* Chain [13]: 0
  with precondition: [0>=A+1] 

* Chain [12]: 2*s(1)+0
  Such that:aux(1) =< A+1
s(1) =< aux(1)

  with precondition: [A>=0] 


Closed-form bounds of f2(A,B,D): 
-------------------------------------
* Chain [14] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [13] with precondition: [0>=A+1] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [12] with precondition: [A>=0] 
    - Upper bound: 2*A+2 
    - Complexity: n 

### Maximum cost of f2(A,B,D): nat(A+1)*2 
Asymptotic class: n 
* Total analysis performed in 55 ms.