/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  : [(div)/4]
1. non_recursive  : [end/3]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [div_loop_cont/4]
4. non_recursive  : [start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into (div)/4
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into div_loop_cont/4
4. SCC is partially evaluated into start/3

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

### Specialization of cost equations (div)/4 
* CE 5 is refined into CE [8] 
* CE 3 is refined into CE [9] 
* CE 2 is refined into CE [10] 
* CE 4 is refined into CE [11] 


### Cost equations --> "Loop" of (div)/4 
* CEs [11] --> Loop 8 
* CEs [8] --> Loop 9 
* CEs [9] --> Loop 10 
* CEs [10] --> Loop 11 

### Ranking functions of CR div(A,B,C,D) 
* RF of phase [8]: [-A+B,B-1]

#### Partial ranking functions of CR div(A,B,C,D) 
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    -A+B
    B-1


### Specialization of cost equations div_loop_cont/4 
* CE 7 is refined into CE [12] 
* CE 6 is refined into CE [13] 


### Cost equations --> "Loop" of div_loop_cont/4 
* CEs [12] --> Loop 12 
* CEs [13] --> Loop 13 

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

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


### Specialization of cost equations start/3 
* CE 1 is refined into CE [14,15,16,17,18] 


### Cost equations --> "Loop" of start/3 
* CEs [15] --> Loop 14 
* CEs [16,18] --> Loop 15 
* CEs [14] --> Loop 16 
* CEs [17] --> Loop 17 

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

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


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

#### Cost of chains of div(A,B,C,D):
* Chain [[8],10]: 1*it(8)+0
  Such that:it(8) =< -A+B

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

* Chain [[8],9]: 1*it(8)+0
  Such that:it(8) =< -A+B

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

* Chain [11]: 0
  with precondition: [C=2,D=B,0>=A] 

* Chain [10]: 0
  with precondition: [C=2,B=D,A>=B] 

* Chain [9]: 0
  with precondition: [C=3] 


#### Cost of chains of div_loop_cont(A,B,C,D):
* Chain [13]: 0
  with precondition: [A=2] 

* Chain [12]: 0
  with precondition: [A=3] 


#### Cost of chains of start(A,B,C):
* Chain [17]: 0
  with precondition: [] 

* Chain [16]: 0
  with precondition: [0>=A] 

* Chain [15]: 2*s(1)+0
  Such that:aux(1) =< -A+B
s(1) =< aux(1)

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

* Chain [14]: 0
  with precondition: [A>=B] 


Closed-form bounds of start(A,B,C): 
-------------------------------------
* Chain [17] with precondition: [] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [16] with precondition: [0>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [A>=1,B>=A+1] 
    - Upper bound: -2*A+2*B 
    - Complexity: n 
* Chain [14] with precondition: [A>=B] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of start(A,B,C): nat(-A+B)*2 
Asymptotic class: n 
* Total analysis performed in 70 ms.