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


--------------------------------------------------------------------------------


WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [f/8]
1. non_recursive  : [end/5]
2. non_recursive  : [exit_location/1]
3. non_recursive  : [f_loop_cont/6]
4. non_recursive  : [sqrt/5]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f/8
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f_loop_cont/6
4. SCC is partially evaluated into sqrt/5

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

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


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

### Ranking functions of CR f(A,B,C,D,E,F,G,H) 
* RF of phase [7]: [-C/2+D/2+1/2]

#### Partial ranking functions of CR f(A,B,C,D,E,F,G,H) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    -C/2+D/2+1/2


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


### Cost equations --> "Loop" of f_loop_cont/6 
* CEs [10] --> Loop 10 
* CEs [11] --> Loop 11 

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

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


### Specialization of cost equations sqrt/5 
* CE 1 is refined into CE [12,13,14,15] 


### Cost equations --> "Loop" of sqrt/5 
* CEs [12,15] --> Loop 12 
* CEs [13] --> Loop 13 
* CEs [14] --> Loop 14 

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

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


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

#### Cost of chains of f(A,B,C,D,E,F,G,H):
* Chain [[7],9]: 1*it(7)+0
  Such that:it(7) =< -C/2+D/2+1/2

  with precondition: [E=2,B=2*A+1,2*F+1=G,B>=0,2*F>=B+1,H>=D+1,D+2*F+1>=H,B+H>=4*F+C] 

* Chain [[7],8]: 1*it(7)+0
  Such that:it(7) =< -C/2+D/2+1/2

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

* Chain [9]: 0
  with precondition: [E=2,2*A+1=B,A=F,2*A+1=G,C=H,C>=D+1] 

* Chain [8]: 0
  with precondition: [E=3,B=2*A+1] 


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

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


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

* Chain [13]: 0
  with precondition: [0>=D] 

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

  with precondition: [D>=1] 


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

### Maximum cost of sqrt(A,B,C,D,E): nat(D/2)*2 
Asymptotic class: n 
* Total analysis performed in 106 ms.