/export/starexec/sandbox/solver/bin/starexec_run_C /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files


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


WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_speed_popl10_simple_single_2_bb1_in/5,eval_speed_popl10_simple_single_2_bb2_in/5,eval_speed_popl10_simple_single_2_bb3_in/5,eval_speed_popl10_simple_single_2_bb4_in/5]
1. non_recursive  : [eval_speed_popl10_simple_single_2_stop/1]
2. non_recursive  : [eval_speed_popl10_simple_single_2_bb5_in/1]
3. non_recursive  : [eval_speed_popl10_simple_single_2_bb1_in_loop_cont/2]
4. non_recursive  : [eval_speed_popl10_simple_single_2_bb0_in/3]
5. non_recursive  : [eval_speed_popl10_simple_single_2_start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_speed_popl10_simple_single_2_bb1_in/5
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is completely evaluated into other SCCs
4. SCC is partially evaluated into eval_speed_popl10_simple_single_2_bb0_in/3
5. SCC is partially evaluated into eval_speed_popl10_simple_single_2_start/3

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

### Specialization of cost equations eval_speed_popl10_simple_single_2_bb1_in/5 
* CE 5 is refined into CE [6] 
* CE 4 is refined into CE [7] 
* CE 3 is refined into CE [8] 


### Cost equations --> "Loop" of eval_speed_popl10_simple_single_2_bb1_in/5 
* CEs [8] --> Loop 6 
* CEs [6] --> Loop 7 
* CEs [7] --> Loop 8 

### Ranking functions of CR eval_speed_popl10_simple_single_2_bb1_in(V_n,V_m,V_y_0,V_x_0,B) 
* RF of phase [7]: [V_n-V_x_0,V_n-V_y_0]
* RF of phase [8]: [V_m-V_x_0,V_m-V_y_0]

#### Partial ranking functions of CR eval_speed_popl10_simple_single_2_bb1_in(V_n,V_m,V_y_0,V_x_0,B) 
* Partial RF of phase [7]:
  - RF of loop [7:1]:
    V_n-V_x_0
    V_n-V_y_0
* Partial RF of phase [8]:
  - RF of loop [8:1]:
    V_m-V_x_0
    V_m-V_y_0


### Specialization of cost equations eval_speed_popl10_simple_single_2_bb0_in/3 
* CE 2 is refined into CE [9,10,11,12] 


### Cost equations --> "Loop" of eval_speed_popl10_simple_single_2_bb0_in/3 
* CEs [12] --> Loop 9 
* CEs [10] --> Loop 10 
* CEs [11] --> Loop 11 
* CEs [9] --> Loop 12 

### Ranking functions of CR eval_speed_popl10_simple_single_2_bb0_in(V_n,V_m,B) 

#### Partial ranking functions of CR eval_speed_popl10_simple_single_2_bb0_in(V_n,V_m,B) 


### Specialization of cost equations eval_speed_popl10_simple_single_2_start/3 
* CE 1 is refined into CE [13,14,15,16] 


### Cost equations --> "Loop" of eval_speed_popl10_simple_single_2_start/3 
* CEs [16] --> Loop 13 
* CEs [15] --> Loop 14 
* CEs [14] --> Loop 15 
* CEs [13] --> Loop 16 

### Ranking functions of CR eval_speed_popl10_simple_single_2_start(V_n,V_m,B) 

#### Partial ranking functions of CR eval_speed_popl10_simple_single_2_start(V_n,V_m,B) 


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

#### Cost of chains of eval_speed_popl10_simple_single_2_bb1_in(V_n,V_m,V_y_0,V_x_0,B):
* Chain [[8],6]: 1*it(8)+0
  Such that:it(8) =< V_m-V_x_0

  with precondition: [B=2,V_y_0=V_x_0,V_y_0>=0,V_y_0>=V_n,V_m>=V_y_0+1] 

* Chain [[7],[8],6]: 1*it(7)+1*it(8)+0
  Such that:it(8) =< -V_n+V_m
it(7) =< V_n-V_x_0

  with precondition: [B=2,V_y_0=V_x_0,V_y_0>=0,V_m>=V_n+1,V_n>=V_y_0+1] 

* Chain [[7],6]: 1*it(7)+0
  Such that:it(7) =< V_n-V_y_0

  with precondition: [B=2,V_y_0=V_x_0,V_y_0>=0,V_n>=V_m,V_n>=V_y_0+1] 

* Chain [6]: 0
  with precondition: [B=2,V_x_0=V_y_0,V_x_0>=0,V_x_0>=V_n,V_x_0>=V_m] 


#### Cost of chains of eval_speed_popl10_simple_single_2_bb0_in(V_n,V_m,B):
* Chain [12]: 0
  with precondition: [0>=V_n,0>=V_m] 

* Chain [11]: 1*s(1)+0
  Such that:s(1) =< V_m

  with precondition: [0>=V_n,V_m>=1] 

* Chain [10]: 1*s(2)+1*s(3)+0
  Such that:s(2) =< -V_n+V_m
s(3) =< V_n

  with precondition: [V_n>=1,V_m>=V_n+1] 

* Chain [9]: 1*s(4)+0
  Such that:s(4) =< V_n

  with precondition: [V_n>=1,V_n>=V_m] 


#### Cost of chains of eval_speed_popl10_simple_single_2_start(V_n,V_m,B):
* Chain [16]: 0
  with precondition: [0>=V_n,0>=V_m] 

* Chain [15]: 1*s(5)+0
  Such that:s(5) =< V_m

  with precondition: [0>=V_n,V_m>=1] 

* Chain [14]: 1*s(6)+1*s(7)+0
  Such that:s(6) =< -V_n+V_m
s(7) =< V_n

  with precondition: [V_n>=1,V_m>=V_n+1] 

* Chain [13]: 1*s(8)+0
  Such that:s(8) =< V_n

  with precondition: [V_n>=1,V_n>=V_m] 


Closed-form bounds of eval_speed_popl10_simple_single_2_start(V_n,V_m,B): 
-------------------------------------
* Chain [16] with precondition: [0>=V_n,0>=V_m] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [15] with precondition: [0>=V_n,V_m>=1] 
    - Upper bound: V_m 
    - Complexity: n 
* Chain [14] with precondition: [V_n>=1,V_m>=V_n+1] 
    - Upper bound: V_m 
    - Complexity: n 
* Chain [13] with precondition: [V_n>=1,V_n>=V_m] 
    - Upper bound: V_n 
    - Complexity: n 

### Maximum cost of eval_speed_popl10_simple_single_2_start(V_n,V_m,B): max([nat(V_m),nat(-V_n+V_m)+nat(V_n)]) 
Asymptotic class: n 
* Total analysis performed in 140 ms.