/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^1))  

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

#### Computed strongly connected components 
0. recursive  : [eval_peed_pldi09_fig4_5_bb1_in/4,eval_peed_pldi09_fig4_5_bb2_in/4]
1. non_recursive  : [eval_peed_pldi09_fig4_5_stop/1]
2. non_recursive  : [eval_peed_pldi09_fig4_5_bb3_in/1]
3. non_recursive  : [eval_peed_pldi09_fig4_5_bb1_in_loop_cont/2]
4. non_recursive  : [eval_peed_pldi09_fig4_5_bb0_in/4]
5. non_recursive  : [eval_peed_pldi09_fig4_5_start/4]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into eval_peed_pldi09_fig4_5_bb1_in/4
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_peed_pldi09_fig4_5_bb0_in/4
5. SCC is partially evaluated into eval_peed_pldi09_fig4_5_start/4

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

### Specialization of cost equations eval_peed_pldi09_fig4_5_bb1_in/4 
* CE 9 is refined into CE [10] 
* CE 8 is refined into CE [11] 
* CE 5 is refined into CE [12] 
* CE 6 is refined into CE [13] 
* CE 7 is refined into CE [14] 


### Cost equations --> "Loop" of eval_peed_pldi09_fig4_5_bb1_in/4 
* CEs [12] --> Loop 10 
* CEs [13] --> Loop 11 
* CEs [14] --> Loop 12 
* CEs [10] --> Loop 13 
* CEs [11] --> Loop 14 

### Ranking functions of CR eval_peed_pldi09_fig4_5_bb1_in(V_n,V_dir,V_i_0,B) 
* RF of phase [10]: [V_i_0]
* RF of phase [11]: [V_i_0]
* RF of phase [12]: [V_n-V_i_0]

#### Partial ranking functions of CR eval_peed_pldi09_fig4_5_bb1_in(V_n,V_dir,V_i_0,B) 
* Partial RF of phase [10]:
  - RF of loop [10:1]:
    V_i_0
* Partial RF of phase [11]:
  - RF of loop [11:1]:
    V_i_0
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V_n-V_i_0


### Specialization of cost equations eval_peed_pldi09_fig4_5_bb0_in/4 
* CE 3 is refined into CE [15] 
* CE 4 is refined into CE [16,17,18] 
* CE 2 is refined into CE [19] 


### Cost equations --> "Loop" of eval_peed_pldi09_fig4_5_bb0_in/4 
* CEs [15] --> Loop 15 
* CEs [18] --> Loop 16 
* CEs [17] --> Loop 17 
* CEs [19] --> Loop 18 
* CEs [16] --> Loop 19 

### Ranking functions of CR eval_peed_pldi09_fig4_5_bb0_in(V_n,V_m,V_dir,B) 

#### Partial ranking functions of CR eval_peed_pldi09_fig4_5_bb0_in(V_n,V_m,V_dir,B) 


### Specialization of cost equations eval_peed_pldi09_fig4_5_start/4 
* CE 1 is refined into CE [20,21,22,23,24] 


### Cost equations --> "Loop" of eval_peed_pldi09_fig4_5_start/4 
* CEs [24] --> Loop 20 
* CEs [23] --> Loop 21 
* CEs [22] --> Loop 22 
* CEs [21] --> Loop 23 
* CEs [20] --> Loop 24 

### Ranking functions of CR eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B) 

#### Partial ranking functions of CR eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B) 


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

#### Cost of chains of eval_peed_pldi09_fig4_5_bb1_in(V_n,V_dir,V_i_0,B):
* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< V_n-V_i_0

  with precondition: [V_dir=1,B=2,V_i_0>=1,V_n>=V_i_0+1] 

* Chain [[11],14]: 1*it(11)+0
  Such that:it(11) =< V_i_0

  with precondition: [B=2,0>=V_dir,V_i_0>=1,V_n>=V_i_0+1] 

* Chain [[10],14]: 1*it(10)+0
  Such that:it(10) =< V_i_0

  with precondition: [B=2,V_dir>=2,V_i_0>=1,V_n>=V_i_0+1] 


#### Cost of chains of eval_peed_pldi09_fig4_5_bb0_in(V_n,V_m,V_dir,B):
* Chain [19]: 1*s(1)+0
  Such that:s(1) =< V_n-V_m

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

* Chain [18]: 0
  with precondition: [0>=V_m] 

* Chain [17]: 1*s(2)+0
  Such that:s(2) =< V_m

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

* Chain [16]: 1*s(3)+0
  Such that:s(3) =< V_m

  with precondition: [V_m>=1,V_dir>=2,V_n>=V_m+1] 

* Chain [15]: 0
  with precondition: [V_m>=V_n] 


#### Cost of chains of eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B):
* Chain [24]: 1*s(4)+0
  Such that:s(4) =< V_n-V_m

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

* Chain [23]: 0
  with precondition: [0>=V_m] 

* Chain [22]: 1*s(5)+0
  Such that:s(5) =< V_m

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

* Chain [21]: 1*s(6)+0
  Such that:s(6) =< V_m

  with precondition: [V_m>=1,V_dir>=2,V_n>=V_m+1] 

* Chain [20]: 0
  with precondition: [V_m>=V_n] 


Closed-form bounds of eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B): 
-------------------------------------
* Chain [24] with precondition: [V_dir=1,V_m>=1,V_n>=V_m+1] 
    - Upper bound: V_n-V_m 
    - Complexity: n 
* Chain [23] with precondition: [0>=V_m] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [22] with precondition: [0>=V_dir,V_m>=1,V_n>=V_m+1] 
    - Upper bound: V_m 
    - Complexity: n 
* Chain [21] with precondition: [V_m>=1,V_dir>=2,V_n>=V_m+1] 
    - Upper bound: V_m 
    - Complexity: n 
* Chain [20] with precondition: [V_m>=V_n] 
    - Upper bound: 0 
    - Complexity: constant 

### Maximum cost of eval_peed_pldi09_fig4_5_start(V_n,V_m,V_dir,B): max([nat(V_m),nat(V_n-V_m)]) 
Asymptotic class: n 
* Total analysis performed in 147 ms.